sketching the history of statistical mechanics and

Sketching the History ofStatistical Mechanicsand Thermodynamics(From about 1575 to 1980)

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Anti-quity

Ideas of atomism, that heat is a modeof motion within bodies and thatpressure is the result of such motion,are all floating around.

1stcentAD

Hero of Alexandria (see also here)writes Pneumatics, an investigationon atmospheric air, summarizing agreat deal of what was known at thetime on syphons, pumps, the effectsof heat on liquids, and enginedesigns.

The aeolipile ofHero

9thcent

Al-Baqilani (d 1013) said to haveintroduced atomism to the MuslimKalam (perhaps influencing Leibniz).

11thcent

The loss of permanent magnetismwhen materials are subjected to hightemperatures known in China.

1575

F Commandine translates Hero ofAlexandria's Pneumatics into Latin(translated earlier in 1547 into Italianby Aleotti).

1612

Santorre Santorio (see here also)(1561-1636) is known to have beenusing an early thermoscope and alsowrites Commentariar in artemmedicinalem Galeni. Santorre writesto Galileo Galilei (1564-1642)including sketches of his device, towhich Galileo replies that it was aninvention of his. The priority remainsunclear.

Sketching the History of Statistical Mechanics a... http://grdelin.phy.hr/~ivo/Nastava/StatistickaFiz...

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1615Thermoscopes of Santorio aresensitive enough to detect near-bybody heat and candles.

1620Johannes van Helmont defines "gas"(the Flemish word for chaos) forair-like substances.

1638

Galileo points out that simple pumpscan only raise water about 32 feet,though this had been commonknowledge to pump makers of thetime.

1641

Ferdinand II, Grand Duke of Tuscany,invents a thermometer using liquid ina glass tube with one end sealed, aslight improvement to Galileo'sthermoscope.

1643Evangelista Torricelli (1608-1647)invents the barometer, also producingthe first partial vacuum.

1644

RenĂ© Descartes' (1596-1650)treatise Principa Philosophiaepublished in Amsterdam. The workextends effords to formulate a fullymathematico-mechanical model ofthe world, including concepts ofnonlocality, the absence of anyvacuum and his vortex model ofatoms.

1647

Gilles Personne de Roberval(1602-1675) performed an oft-quotedexperiment on air pressure wherebya carp's swim-bladder is partiallyremoved, squeezed of almost all airand tied shut. The carp is then placedin a Torricellian vacuum and thebladder is observed to expand.

1648

Florin Perrier experimentally showsthat the height achieved by mercuryin a barometer decreased as onescaled a mountain, a theoretical


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prediction of his brother-in-law,Blaise Pascal, and also known asthe Puy de DĂ´me experiment.

ca1650

(Coffee begins to be important to andcatch on in Europe.)

1651

Jean Pecquet's (1622-1674) book onpsychology popularizes the Robervalexperiment (English translation in1653). He also introduces the term"elater" as the tendency of air toexpand, and theorizes that air on theearth's surface is compressed by theweight of the atmospheric air.

1654

Otto von Guericke's (1602-86)experiment with two ironhemispheres held together by astrong partial vacuum being strongenough to resist the pull of a train ofhorses on either side.

Ferdinand II invents the sealedthermometer.

1660

Robert Boyle (1627-91) publishesNew Experiments Physio-Mechanicall, touching the Spring ofthe Air, and its Effects. Oneexperiment clearly shows thedependency on Torricelli's vacuum onambient air pressure. Also presentedare discussions of both Pecquet's ideaof air modelled by coiled-up wool-likeor spring-like atoms (which waspreferred by Boyle) and ofDescartes' idea of whirling particleswhich repell one another at shortdistances.

In response to Boyle's ideas,Franciscus Linus (1595-1675)proposes a theory whereby a vacuumis explained by the creation of an

Robert Boyle


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invisible collection of thread-like"funiculus," which strive to holdnearby objects together.

Richard Townley (1628-1707) andHenry Power's (1623-1668)experiments establishing the PV lawfor expansion (the so-called "Boyle'sLaw" or "Marriotte's Law").

1661

Boyle adds an appendix to his 1660work, responding to the criticisms ofLinus and Thomas Hobbes,presenting improved experimentalresults and giving a version of what isnow known as "Boyle's Law" for thecase of compression.

1662Boyle's "Defense of the Doctrinetouching the Spring and Weight ofthe Air."

1663

Blaise Pascal (1623-1662) writes Onthe Equilibrium of Liquids (publishedposthumously) suggesting thatpressure is transmitted equally in alldirections in a fluid (later known as"Pascal's law"), probably discoveredaround 1648.

Power's book ExperimentalPhilosophy, publishing early resultson the PV law.

1669

Johann Joachim Becher'sSubterranean Physics, a tract onalchemy and experimental results onminerals, introduces the idea that a"terra pingus" (oily earth) causes fire.(This idea is later picked up to formthe phlogiston theory of heat.)

1670

Boyle discovers that when acidinteracts with certain metals aflammable gas is produced, knownnow as Hydrogen.


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1673Christiaan Huygens (1629-95)builds a motor driven by theexplosion of gunpowder.

1674

John Mayow suggests that air mayconsist of two different gases fromexperiments done on mice andcandles, reported in his Five Medico-Physical Treatises.

1676

EdmĂ© Mariotte (~1620-1684)independently finds relationshipbetween pressure and volume, in hiswork On the Nature of Air. (Known as"Mariotte's law" in France, and"Boyle's law" elsewhere.)

1685Mariotte's The Motion of Water andOther Fluids published(posthumously).

1690Denis Papin (1647-1712) uses steampressure to move a piston for the firsttime.

1697Georg Ernts Stahl introduces the ideaof phlogiston as the agent of burningand rusting.

1702

Guillaume Amontons extrapolates theidea of absolute zero from theobservation that equal drops intemperature produce equal drops inpressure, and since pressure cannotbecome negative, there must be alower limit to temperature.

Ole Christensen RĂ¸mer devises atemperature scale based on the twophenomena of the boiling point ofwater and the temperature at whichsnow begins to form.

1705Francis Hauksbee shows that soundneeds air for propagation.

1712 Thomas Newcomen's steam engine.


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1714Gabriel Fahrenheit's mercurythermometer introducing histemperature scale. (see notes)

1716

Jakob Hermann (1678-1733)proposes the first definite measure ofthe heat of molecular motion in hiswork on rational mechanics,Phoronomia. He postulates that (inmodern lingo) pressure isproportional to density and to thesquare of the average velocity of theparticles of motion.

Jakob Hermann1723

Stahl's Foundations of Dogmatic andExperimental Chemistry popularizesphlogiston and the ideas of JohannBecher.

1724Hermann Boerhaave proposes thatheat is a fluid of some sort.

1729

Leonhard Euler (1707-1783),extending Johann Bernoulli's workon Descartes' vortex cosmology,models air with tightly-spaced,spinning spheres. He formulate anequation of state relating humidity,pressure, density and velocity, findingthe Townley-Power-Boyle law as anapproximation. He calculates airmolecules to be about 477 m/s atmean conditions, and that this isabout the speed of sound.

1730Johann Juncker's Conspectus ofChemistry systematically expandsphlogiston theory.

1733

Daniel Bernoulli (1700-1782), in atreatise on hydrodynamics workedout in the period from 1728 to 1733,gives a derivation of the gas lawsfrom a billiard ball model, derives theBoyle-Mariotte relation and usedconservation of mechanical energy to Daniel Bernoulli


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show that as temperature changesthe pressure will changeproportionally to the square of theparticle velocities. This text marksthe first truly statistical treatment ofkinetic theory. A significantly updatededition of the text is published in1738. The paper is all but forgottenuntil 1859.

1739

George Martine establishes that thevolume of an object is notproportional to the amount of heat ithas.

1742

Anders Celsius (1701-1744)publishes "Observations on twopersistent degrees on athermometer," basing his scale on thefreezing point (100 degrees) andboiling points (0 degrees) of water.(The system is reoriented in 1745 byCarl Linnaeus, a.k.a. Carl vonLinnĂ©.)

1744

Mikhail Vasilievich Lomonossovpublishes a paper on the causes ofheat and cold, stating that heat is aform of motion.

1744(also, Carl von LinnĂ©, 1707-1778)reorients Celsius's scale.

1748

Lomonosov formulates laws ofconservation of energy and mass.Through about 1760, he performs anumber of theoretical investigationsabout molecular structures,speculating on the effects oftranslation, vibration, and rotationsof such molecules.

1756

William Cullen's An Essay on the ColdProduced by Evaporating Fluids andsome Other Means of ProducingCold.


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1758

Rudjer Giuseppe Boskovic(1711-1787) mathematically modelsmolecules via points subjected tointermolecular forces which areattractive nearby but repulsive atgreater distances. His efforts,however, are too vaguely worked outto base a theory on.

1761

Joseph Black (1728-1799) finds thatwhen melting ice, heat can beabsorbed without changingtemperature.

1765James Watt invents his steam engine,which is over six times more effectivethan Newcomen's.

1772Johan Carl Wilcke calculates thelatent heat of ice.

Phlogiston Theory (~1660's to ~1790's)Kinetic Heat Theory (~1716 to ~1760's) (then ~1816 to present)Caloric Heat Theory (~1780's to ~1860's)Wave Theory of Heat (~1830's to ~1860's)

Statistical Mechanics (~1850's to present) (Bernoulli excepted)Quantum Statistics (~1900's to present)

1781Wilcke comes up with the concept ofspecific heats.

1782

Lavoisier establishes an early versionof the conservation of matter throughhis finding of constancy of weightbefore and after chemical reactions.

1783

Lavoisier's work, Reflections onPhlogiston, on the weaknesses ofphlogiston theory with respect tocombustion.

1786Lavoisier and Laplace's workMemoir on Heat.

1787

Jackues-Alexandre Charlesdetermines that at a giventemperature change, different gasesexpand the same amount (known as"Charles's law").

1789Lavoisier's book Elementary Treatiseon Chemistry, containing the law ofmass conservation.


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1791

Richard Kirwan (~1733-1812),previously a staunch defender ofphlogiston theory, concedes that theexperimental evidence saysotherwise.

Pierre PrĂ©vost's theory of heat andradiation exchange, stating that coldis the absence of heat, hot bodiesradiate continually and that a lack ofradiation indicates equilibrium withsurroundings temperature.

Jeremias Richter (1762-1807) foundsstoichiometry, the principle of fixedchemical reactions.

1798

Cannon-boring experiments ofBenjamin Thompson (CountRumford) (1753-1814)demonstrating the conversion ofwork into heat in his work EnquiryConcerning the Source of Heat whichis Excited by Friction, showing alsothat additional weight of an objectdue to heating (a prediction of calorictheory) was not detected.

1799

Ice-rubbing experiments ofHumphrey Davy (1778-1829)demonstrating the conversion ofwork into heat, and suggesting thatan indefinite amount of heat could begenerated from a body (whereascaloric theory severely limits itsavailable amount).

Joseph-Louis Proust formulates thatelements in a compound alwayscombine in definite mass ratios("Proust's Law").

1800William Herschel (1792-1871)publishes "An investigation of thepowers of prismatic colours to heat


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and illuminate objects" investigatingthe effects of different wavelengths oflight on a thermometer, finding lightjust beyond the red to be the hottest.

1801

Johann Ritter discovers ultravioletradiation while doing work with silverchloride.

John Dalton (1766-1844) finds thattwo gases in the same region producethe same pressure as if they occupiedthe region alone, known as the law ofpartial pressures.

1802

Joseph-Louis Gay-Lussac (1778-1850)finds that, at a given pressure, thechange in volume is proportional tothe change in temperature.

1803

Dalton formulates his atomic theoryof matter, stating that chemicals areformed by integer numbers of atoms,by studying the weights of chemicalsand reactants.

Claude-Louis Berthollet demonstratesthat reaction rates depend on boththe amount of substances present aswell as their affinities in his workEssay on Static Chemistry.

William Henry finds that a gas's masswhen dissolved in a liquid isproportional to the pressure (laterknown as "Henry's law").

1804

John Leslie (1766-1832) writes AnExperimental Inquiry into the Natureand Propagation of Heat, showingthat light and radiated heat havesimilar properties.

1805Pierre-Simon Laplace (1749-1827)formulates his theory of capillaryforces based on his studies of


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molecular forces in liquids.

Pierre-SimonLaplace1806

Thomas Young (1773-1829)formulates a precursor to the modernformulation of energy,mathematically associating it withmv2 (twice the modern "kineticenergy").

Young's System of Chemistrycontains the first published accountof Dalton's ideas on atomic theory.

1807

Jean Baptiste Joseph Fourier(1768-1830) completes his On thePropagation of Heat in Solid Bodies,introducing many mathematicalnovelties, including his seriesexpansion techniques.

Jean Fourier

1808(Dec 31st) Gay-Lussac states thatgases chemically combine in exactproportions of volume.

1811

SimĂ©on-Denis Poisson(1781-1840) develops hismathematical theory of heat, basedon the work of Fourier.

Amedev Avogadro (1776-1856)hypothesizes that the "number ofintegral molecules in any gases is [...]always proportional to the volumes",and that the ratio of the masses ofmolecules is proportional to the ratioof gas densities at equal temperatureand pressure (later becoming"Avogadro's law").

JĂ¶ns Jakob Berzelius states thatelectrical and chemical forces areone and the same and that atoms areelectrically charged, in his workTheory of Chemical Proportions andthe Chemical Action of Electricity.


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1812

Davy writes Elements of ChemicalPhilosophy, including a hypothesisthat in addition to the vibrational andundulatory motion of solids, gasses aswell exhibit rotational motion aboutan axis.

Delaroche and BĂ©rard'smeasurements of specific heats atatmospheric pressure of a largenumber of gasses. Theirmeasurements agreed withLaplace's predictions and remaineda cornerstone for caloric theory.

1816

John Herapath (1790-1868) writes,"On the physical properties of gases,"essentially proposing the sametheory, but developed independently,as that of Daniel Bernoulli.

1819

Pierre-Louis Dulong and AlĂ©xisThĂ©rĂ¨se Petit (1791-1820) findconstant specific heat at constantpressure for metals over wide rangeof temperatures, finding that theproduct of the specific heat and theatomic mass remains constant(known as the "Law of Dulong andPetit").

1821

Herapath publishes, "A mathematicalinvestigation into the causes, laws,and principal phaenomena of heat,gases, gravitation, etc," in the Annalsof Philos. He explained in outline howkinetic theory could give accounts ofsound propagation, phase changesand diffusion. The paper is all butignored due to rejection by the RoyalSociety of London, and HumphryDavy in particular.

Thomas Johann Seebeck discovers aprocess by which heat is converted


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into electricity in the junction of somemetals, known as theormoelectricity.

1822

Fourier's essay Analytic Theory ofHeat is published, furthering histechniques of analysis.

Charles Cagniard de la Tour, inliquification experiments, finds thatboth temperature and pressure mustbe appropriately controlled, anddiscovers what is now know as thecritical point of a substance.

1824

Sadi Carnot (1796-1832) publishes"Reflections on the Motive Power ofFire," introducing the ideal gas cycleanalysis, showing that when heatpasses between two bodiestheormodynamic work (which hedefines) is done, and proposes anidea for an internal combustionengine.

Pierre-Simon Laplace (1749-1827)publishes several papers refining anidea of Newton's that gasses areformed through repulsiveinteractions.

Sadi Carnot

1827

Robert Brown (1773-1858),investigating the well-knownirregular motions seen of particlessuspended in liquid under amicroscope, shows that such motionscannot be attributed to any vitality ofthe particles themselves, throughstudies of many organic andinorganic substances.

1829

Gustave-Gaspard Coriolis defines theterm "kinetic energy" in his studiespublished as On the Calculation ofMechanical Action.


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Thomas Graham (1805-1869)experimentally uncovers the law ofgas diffusion, by which the rate of agas's diffusion, squared, isproportional to its density.

1833Heinrich Friedrich Emil Lenzdetermines that resistence in metalsincreases with temperature.

William Thomson1834

Clapeyron formulates the first versionof the second law of thermodynimcs,based on studies of steam engines.

Jean-Charles-Athanase Peltier showsthat heat can be absorbed or givenoff when current is passed one way orthe other across a junction betweentwo different metals (knows as thePeltier effect).

1837

von Suerman's experiments on air atreduced pressures verifyingClappeyron's version of Carnot'sformulas.

The 1840's were markedby the nearlysimultaneous andindependentconceptualization of theconservation of energy byMayer, Joule ,Helmholtz and LudvigAugust Colding(1815-88).

1842

Julius Robert Mayer (1814-1878)clearly formulates the conservation ofenergy, and that heat is a form of(mechanical) energy.

William Thomson, Lord Kelvin 's(1824-1907) On the Uniform Motionof Heat in Homogeneous SolidBodies.

1843

(through 1848) Through a series ofexperiments, James Prescott Joule(1818-1889) establishes the exactrelationship between heat andmechanical work. (Joule's work islittle read.)

John James Waterston (1811-1883)anonymously publishes Thoughts onthe Mental Functions containing in a


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note at the end a full and accurateaccount of the kinetic theory of gasesand the introduction of the idea of amean free path. The work goes all butcompletely unread.

1845

Waterston submits a papers on thekinetic theory of gases to the RoyalSociety, who rejects it. The paperprecisely lays out the ideas of energyequipartition and gives the firstmodern kinetic definition oftemperature. A short abstractappears a year later, and again in1851, but the work is ignored.

1847

Joule publishes "On Matter, LivingForce, and Heat" in the ManchesterCourier, stating the principle of theconservation of energy and giving theconversion from heat to kineticenergy.

Hermann Ludwig Ferdinand vonHelmholtz (1821-94) publishes hisOn the Conservation of Energy,extending Carnot's princple of the'impossibility of unlimited movingforce' (kinetic energy) to amathematical formulation of the'principle of conservation of livingforce' (vis viva / kinetic energy).(Independent of Joule's publications.)

John William Draper finds that allsubstances begin to glow around525Â°C, starting in the red andeventually becoming white.

James Joule

1848

Joule reads a paper using Herapath'skinetic theory. The paper contains thefirst numerical results from thekinetic theory. (Not published until1851, and not well known untilClausius's reference to it in 1857.)


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William John Macquorn Rankine 's(1820-1872) researches intomechanics and heat (mainly through1855).

Kelvin develop's a scale of absolutetemperature (now known as the"Kelvin" scale) based on the theory ofCarnot.

1849

James Thomson (1822-1892), usingCarnot's theories, predicts the lowerof the freezing point of water underhigh pressures.

Kelvin, in speaking of Carnot'stheory, coins the term"thermodynamics."

1850

John Herschel (1792-1871)publishes (anonymously, thoughgenerally known) an article onQuetelet's work in statistics,introducing much of the continentalwork on statistics to Britishscientists.

Rudolf Clausius (1822-88) gives averbal formulation of the second law,for which there is no mechanismwhose only function is the transfer ofheat.

Hermann vonHelmholtz

1851

Kelvin independently rediscovers theidea of absolute zero (149 years afterAmontons), extrapolating fromCharles' law that it must be about-273Â°C, and suggesting that theenergy of the molecules would tendto zero. He also derives the secondlaw of thermodynamics usingCarnot's ideas.


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1852

Henri-Victor Regnault (1810-1878)shows that gas behavior doesn't quitefollow Boyle's law at lowtemperatures and extrapolates avalue of -273Â°C for absolute zero.

Joule and Kelvin show thatexpanding gases become cooler inthe process, the latter giving the firstgeneral statement of the principle ofthe "universal tendency towarddissipation of energy."

1854

Hendrik Roozeboom experimentallydetermines the phase law, laterderived mathematically by Gibbs.

Clausius proposes the function dQ/Tas a way to compare heat flows withheat conversions.

Rudolf Clausius

1855Rankine's Outlines of the Science ofEnergetics.

1856

Karl KrĂ¶nig (1822-79) writes apaper suggesting that gas moleculesin equilibrium travel in straight linesuntil they collide with something,published in Poggendorfs Annalender Physik. Whereas the efforts ofBernoulli, Euler, Herapath, Hermannand Joule were largely ignored, KarlKrĂ¶nig's efforts were widely read,though not constituting an advance inkinetic theory.

1857

Clausius publishes a paper on amathematical kinetic theory,explaining evaporation andestablishing heat as energydistributed statistically amongparticles.

1858Clausius introduces the idea of themean free path of a particle inworking out a kinetic theory of


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diffusion.

1859

James Clerk Maxwell (1831-79)reads a paper on kinetic theory,printed in 1860 as "Illustrations ofthe Dynamical Theory of Gases,"using random velocity distributionsfor gases, and showing viscosity to beindependent of temperature. Thepaper is originally intended to showinternal inconsistencies in the kinetictheory, but through its rigor it greatlyrefined the theory and provided newinsights.

Gustav Robert Kirchhoff(1824-1887) derives from the secondlaw of thermodynamics that objectscannot be distinguished by theirthermal radiation at a given uniformtemperature, one must also usereflected light.

Bernoulli's paper republished due torenewed interest in kinetic theory.(Herapath henceforth goes intoobscurity.)

James ClerkMaxwell

1860

Michael Faraday's paper "PressureMelting Effect" describing thelowering of the freezing point ofwater using pressure.

Maxwell shows a discrepancybetween the prediction by kinetictheory of the specific heat of diatomicgases and experiment. (Not to beresolved satisfactorally until the earlystages of quantum theory.) This paperis the first of four works on kinetictheory by Maxwell, bringing a newlevel of rigour and sophistication tothe theory.


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1861

Thomas Andrews (1813-1885), in aseries of experiments with CO 2

through 1869, finds that at lowtemperatures Boyle's law breaksdown, and there are regions on a PVchart where, for a given isotherm,changes in volume produce nochange in pressure. This region isrecognized to be the liquid-vapourequilibrial state. He rigorously findsthe critical point and triple point.

Kirchhoff formulates the notion of ablackbody.

1863

John Tyndall's (1820-1893) Heat as amode of Motion, popularizingMaxwell's ideas on heat.

Andrews shows that, contrary toexpectations, above a substance'scritical point it may be continuouschanged from gas to liquid and viceversa through variations oftemperature and pressure.

1865

Clausius uses Carnot's techniquesto derive "entropy" (and shows thetwo laws of thermodynamicsexpressible in the same ways as theolder caloric theory), a term coinedfor the quantity defined early by him,dQ/T. In a public speech entitled "Theentropy of the universe tends to amaximum," he shows howthermodynamics seem to imply aneventual heat death for the universe.

Josef Loschmidt's (1821-95) pointsout that Maxwell's conclusion thatthe proportionality of the mean freepath to V/Nd2 could be used toestimate the size of an atom. Withfurther considerations, he estimates


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the size of an air molecule to beabout 10-7 cm, about 4 times toolarge, but the best estimate to date.

1866Maxwell models interatomic forcesby a inverse fifth-power law, thoughonly as an interim solution.

1867

Maxwell publishes his major work onkinetic theory, On the DynamicalTheory of Gases.

Kelvin's On Vortex-Atoms.

(Spurred on by Maxwell's work,serious debates on the statisticalinterpretation of irreversibilitybegin.)

1868

Ludwig Boltzmann's (1844-1906)extends Maxwell's distribution law toinclude external forces. In the case ofgravity, he worked through thedistribution of densities andpressures and that thermalequilibrium was maintained.

LudwigBoltzmann

1871

Maxwell, helping out P G Tait, whowas drafting an textbook onthermodynamics, comes up with hisparabol of the daemon toconceptually explain heat statistics.

Boltzmann suggests that one mayderive the probabilistic picture fromthe kinetic one by heuristicallyassuming that all microstates must berealized in a system before returningto a specific microstate, and thusmeasured values should average theeffects of such states. (Known as the"ergodic theorem," and so named byEhrenfest in 1911.)

James Thomson suggests that even


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below the critical point, a substancemay smoothly transition between gasand liquid from considerations ofexperimental data on pressure andvolume.

1872

In a 100-page paper entitled,"Further Studies of the ThermalEquilibrium of Gas Molecules,"Boltzmann's derives his transportequation (Î—-Theorem), showingexplicitly that isolated systems mustalways evolve in such a way thatentropy increases. He introduces anumber of mathematical innovations,including a technique of discretizingthe allowed energy levels for amolecule, and allowing this energybin to go to zero. Little read at first,the paper later meets withwide-spread opposition.

1873

Josiah Willard Gibbs (1839-1903)publishes Graphical Methods in theThermodynimcs of Fluids and AMethod of GeometricalRepresentation of theThermodynamic Properties ofSubstances by Means of Surfaces,introducing many new graphicaltechniques. From 1873 to 1878 hepublishes a series of importantarticles in the Transactions of theConnecticut Academy of Arts andSciences, widely influencingscientists in the US and in Europe.

Johannes Diderik van der Waals(1837-1923), in doctoral dissertation,gives the first correct approximationfor the effects of a non-vanishingratio of molecule diameter to averagedistance by assuming long-rangeattractive and short-range repulsive

Josiah Gibbs


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forces, applying this to the case ofgases at high densities. Using his"equation of state," he gives the firstsuccessful attempt to explain a(gas-liquid) phase transition. Thetheory both accounted for Andrews'scritical point phenomena andconfirmed James Thomson'shypothesis.

1874

Kelvin points out that theirreversibility of Boltzmann's kinetictheory seems to contradict theunderlying classical laws of physicsremaining time-invariant (theso-called "reversibility paradox,"sometimes attributed to Loschmidt).

1876

Gibbs publishes the first part of Onthe Equilibrium of HeterogeneousSubstances (the 2nd part in 1878).The works deal with chemicalreactions, phase equilibrium and theuse of free energy.

(Karl Paul Gottfried von Linde buildsthe first practical refrigerator usingliquid ammonia.)

1877

Boltzmann formulates a statisticalmechanical version of the second lawof thermodynamics in the paper, "Onthe Relation Between the Second Lawof the Mechanical Theory of Heat andthe Probability Calculus with Respectto the Theorems on ThermalEquilibrium". There he formulatesthat the entropy of a system isproportional to the log of the phasespace volume occupied by themacrostate of the system, S = k lnÎ©, making use of his mathematicalinnovation of using finite areas ofphase space.


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Liquification of oxygen achieved,after nearly one hundred years oftrying, by Louis Paul Cailletet(1832-1913) (on Dec 2nd) and RaoulPierre Pictet (1846-1929) (on Dec22nd).

1879

Josef Stephan (1835-1893)determines that the amount ofradiation given off by a body throughheating is proportional to the fourthpower of its temperature (known asthe "Stephan-Boltzmann law"), RĎ„ =ĎT4.

1884

Boltzmann (1844-1906) succeeds intheoretically deriving the radiationlaw found by Stephan, showing that amechanical pressure and energydensity must be associated with theradiation in order to satistfy thesecond law.

Gibbs coins the term "statisticalmechanics" for the kinetic theory'streatment of thermodynamic issues.

1885

Lodge promotes the idea thatmechanical energy can be localizedand flow, as inspired by the work ayear earlier by Poynting inelectromagnetic theory.

Johann Jakob Balmer (1825-1898)finds a formula for describing thefour spectral wavelengths thenknown for hydrogren as found byĂ…ngstrom.

1889

Jules Henri PoincarĂ©(1854-1912) derives his recurrencetheorem, whereby a system with fixedtotal and volume will eventuallyreturn arbitrarily closely to any givenstate.


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Gibbs' last work, ElementaryPrinciples in Statistical Mechanics.

1890

Edward Parnell Culverwell(1855-1931) points out the apparentcontradiction between Boltzmann'sH-theorem and the irreversibility ofthe micromechanical processes onwhich it is based, suggesting thatsome kind of irreversible processtakes place at this micro level,perhaps in connection with the ether.

1893

Wilhelm Carl Werner Otto FritzFranz Wien (1864-1928)experimentally finds that thewavelength of maximum radiation ofthermal body is proportional to theinverse of its temperature (known as"Wien's law") using an oven with asmall hole as an approximation to atheoretical black-body.

1894

S H Burbury points out that theH-theorem relies on the uncorrelatednature of molecular interactions, butthat this may not be valid after anindividual collision, and hence not ingeneral valid without some externalrandomizing element. Boltzmanncalls this the hypothesis of moleculardisorder, specifically referring to thelow probabilitiy of two moleculescolliding twice within any significanttime frame, but mentioning that thiswould become an issue for gases athigh densities.

1895

Pierre Curie (1859-1906), in hisdoctoral dissertation, defined bothferro-, dia-, and paramagnetism,showing that ferromagnets lose theirmagnetic properties as theirtemperature is increased, eventually


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losing it completely above a certaintemperature specific to that material(the "Curie point"). He suggests thatdiamagnetism is an atomic property,while the other two are properties ofbulk matter.

Wilhelm RĂ¶ntgen (1845-1923)discovers a new penetrating kind ofradiation, dubbed X-rays.

1896

Ernst Zermelo (1871-1953), startingwith the postulate that the secondlaw is true, tries to show the inherentcontradictions of the purelymechanical basis of statisticalmechanics, making use ofPoincarĂ© 's result on recurrence(his "recurrence paradox").

Wien proposes an explicit form forthe black body distribution law, Ď =Î±Î˝3exp{-Î˛Î˝/T}, which fit theexisting data.

Antoine Henri Becquerel(1852-1908) discovers radioactivity influorescent materials.

1897

Joseph John Thomson (1856-1940)demonstrates that cathode rays wereelectrically charged particle streams,know shortly thereafter as electrons.

Max Planck

1898Boltzmann publishes his Lectureson Gas Theory.

1899

Otto Lummer (1860-1925) andErnst Pringsheim complete the firstaccurate measurements of thespectral radiancy of blackbodies,showing the breakdown of Wien's lawat high temperatures and lowfrequencies.


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Emile Hilaire Amagat publishes TheLaws of Gases of extensiveexperiments with gases under veryhigh pressures.

JJ Thomson and Philipp Lenard(1862-1947) begin experimentalinvestigations of photoelectricradiation.

1900

Kelvin proposes a modification toWein's law of the form Ď ~Î˝2exp{-Î˛Î˝/T}.

Max Karl Ernst Ludwig Planck(1858-1947), studying blackbodyradiation and following Boltzmann'stechniques of dividing the energycontinuum into cells, proposes fixingcell sizes to be proportional tooscillator frequency, and in so doingderives the correct radiationspectrum for blackbodies. Planckproposes the constant, h (Planck'sconstant), as a quantum of action inphase space.

Planck's 1900 analysisdid not, at the time, implyany new law about themicrostructure of matter,nor was there any reasonto believe thatextrapolation of theRayleigh-Jeans lawsignalled any failure ofclassical methods.

1902

Gibbs publishes ElementaryPrinciples in Statistical Mechanics,his treatise on the subject, derivingcommon thermodynamic propertiesfrom particle statistics, giving his fullaccount of ensemble theory and theirrelationships (including the so-called"Gibbs paradox," though there wasnothing paradoxical about it at thetime).

1905

Marian von Smoluchowski andAlbert Einstein (1879-1955)independently investigate Brownianmotion, the motion of very smallparticles suspended in liquid. This isshown to be an observable effect ofthe fluctuations of statistical


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mechanical movement, despiteproducing no net effect on average.

Einstein publishes a paper on thephotoelectric effect, basing hisanalysis on an analog of thestatistical mechanical approach forclassical electromagnetic fieldsmodelled as quanta of light.

Paul Langevin (1872-1946) developesa more satisfactory theory of para-and diamagnetism, applyingstatistical mechanics to gases ofmolecules with permanent dipolemoments, also explaining the inversetemperature dependence ofparamagnetic susceptibility, thoughlater shown by Bohr to beinconsistent with statisticalmechanics obeying classicalmechanics.

1906

Walther Nernst (1864-1941)formulates his "heat theorem,"stating that in the limit of absolutezero temperature, both the entropychange and the heat capacity go tozero (subsequently recognized as theThird law of thermodynamics).

Pierre Weiss (1865-1940) createsgeneral theory of paramagnetic toferromagnetic transitions.

Albert Einstein

1907

Andrei Andreyevich Markov(1856-1922) develops his theory oflinked probabilities.

Einstein publishes a paper on thespecific heats of solids, deriving thelaw of Dulong-Petit from atomicoscillators confined to quantizedenergies, working out well with the


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recent theorem of Nernst.

Pierre Weiss explains ferromagnetismby way of small domains of magneticpolarization within a material.

1908

Jean-Baptiste Perrin calculates theapproximate size of a water moleculein experimental tests of Einstein'swork on Brownian motion, furtherconvincing many of the atomichypothesis.

Planck begins formulatingderivations of the black-body lawstarting with an assumption of energyquantization.

JJ Thomson solidifies his "plum-pudding" model of the atom.

1909

Constantin CarathĂ©odorypublishes a purely mathematical andaxiomatic account ofthermodynamics.

Einstein corrects the blackbodyderivation of Planck, which wastechnically only valid for hÎ˝<<kT.

1910

Jean Perrin experimentally showsthat the theoretical predictions ofEinstein's calculations on Brownianmotion are in agreement, becomingfor many the best extant proof of theexistence of atoms.

1911

Ernst Rutherford (1871-1937)proposes the nuclear model of theatom.

Planck's first paper explicitlyquantizing the allowed radiation ofoscillators in a blackbody.


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Arnold Sommerfeld (1868-1951)notes that elementary regions ofphase space should be related toPlanck's constant.

Otto Sackur (1880-1914) suggeststhe need for an absolute definition ofentropy, in order that quantumsystems be taken into account(suggesting that phase space bedivided into cells of volume h3).

Ladislaw Natanson proposes thatPlanck's law is the result of theindistinguishability of states of lightquanta.

Niels Henrik David Bohr(1885-1962) defends his dissertationand begins constructing atomicmodels which try to forge aconnection with Planck's constant asa fundamental constant ofquantization.

Heike Kamerlingh Onnes (1853-1926)experimentally finds that mercurywill become superconductive whencooled very close to absolute zeroand also discovers superfluidity.

Paul (1880-1933) and TatianaAfanassjewa Ehrenfest (1876-1964)publish a work giving a detailedcriticism of the ensemble theories instatistical mechanics.

Nernst's experiments with manysubstances, shows specific heatsgoing to zero at absolute zero ingeneral, providing strong support forthe new quantum theories.


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1912

PoincarĂ© proves that one caninvert the Planck distribution via aFourier transform and deduce thatblack-body radiation implies aquantization of energy states.

Sackur and H Tetrode independentlysolve Boltzmann's Law to obtain

S = Nk ln[(2ĎmkT)(3/2)V/Nh3] +(5/2)Nk

showing a need for quantization inclassical gas laws.

1913

Artur Rosenthal (1887-1959) andMichel Plancherel (1885-1967) provethat the ergodic hypothesis is notviable for any dynamical system(opening the way to the quasi-ergodichypothesis and certain theorems inergodic theory).

Paul Ehrenfest shows how to estimaterotational effects of a diatomic gas onspecific heat by replacing integralswith sums over discrete contributionsfrom quantized states. The work islater refined by E Holm (1913) and byPlanck (1915).

Bohr's article, "On the Constitutionof Atoms and Molecules."

1916

Robert Andrews Millikan(1868-1953), in experiments with thephotoelectric effect, both confirmsthe theoretical work of Einstein andconfirms the value of Planck'sconstant independent of work donewith blackbodies.

Einstein produces a derivation ofthe black-body radiation distributionwith the assumption of bothspontaneous as well as stimulated


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emission of radiation by matter.

Nernst predicts a state ofdegeneration can be reached for anygas at a low enough temperature,through extensions of histhermodynamic theory.

Sydney Chapman (1888-1970) andDavid Enskog (1884-1947) developways to solve the Maxwell-Boltzmanntronsport equations for a generalclass of inter-molecular force laws.

Gilbert Newton Lewis (1875-1946)devises a theory of molecularbonding based on atoms consisting ofa series of concentric cubes, theedges of which may share electronswith other atoms. (The idea ispopularized, starting in 1919, byIrving Langmuir (1881-1957).)

1917

Arthur Stanley Eddington(1882-1944) publishes a paper onradiative equilibrium, suggesting thatthe ionization of atoms in stars.

1920

Meghnad Saha (1893-1956) writes,"Ionization in the solarchromosphere," analyzing spectrallines of stars as atomic dissociation inthe chromosphere, where lowerpressures override the lowertemperatures of a star, also (in asecond paper) predicting that lower-temperature sun-spots will show linesof rubidium and cesium (an effectdetected in 1922 by H N Russell).

Wilhelm Lenz (1888-1957) modelscrystals by a lattice of dipolar atomswhich feel nearest-neighborinteractions, obtaining the Curie law


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for magnetization and suggestions itsapplications to ferromagnetism.

1922

Louis Victor Pierre Raymond ducde Broglie (1892-1987) appliesSackur's technique of quantizingphase space to derive the Wiendistribution law for energy density:

du = (8Ďh/c3) exp(-hÎ˝/kT) Î˝3 dÎ˝

Charles Darwin (1887-1962) andRalph Howard Fowler (1889-1944)publish "On the partition of energy,"developing a new approach toevaluating statistical probabilitiesusing complex analysis and themethod of steepest descent.

1923

Lewis's Thermodynamics and theFree Energy of Chemical Substances,bringing thermodynamics in closercontact with chemistry.

SatyendranathBose

1924

(June) Satyendranath Bose(1894-1974) sends Einstein a copyof his paper, containing a newderivation of Planck's radiation lawbased purely on photon statistics,after it was rejected by PhilosophicalMagazine. Einstein translates it intoGerman and submits it to theZeitschrift fĂĽr Physik for him with arecommendation.

Einstein presents a paper showingthat in the limit of high temperatures,a gas of indistinguishable Boseparticles approaches thecharacteristics of a Boltzmann gas.

de Broglie writes two papers in theComptes rendus of the Paris Academyelaborating on a fundamentalprinciple of wave-particle duality. The


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works mature into his 1925 doctoralthesis.

1925

Max Born (1882-1970), WernerKarl Heisenberg (1901-1976), andPascual Jordan formulate quantummechanics based on the mathematicsof matrix algebra.

Einstein, citing works by Bose andde Broglie, suggests that theanalogy between quantum gases andmolecular gases are complete, andthat both photons and molecules haveboth particle and wavecharacteristics. He also points outthat molecules at low temperaturescannot be considered independententities, even in the absence ofintermolecular forces, and will form aquantum condensate.

Samuel A Goudsmit's (1902-1979)hypothesis an extra degree offreedom to electrons termed "spin"due to the mathematical similarity toclassical spin. Later, with GeorgeEugene Uhlenbeck (1900-1988),half-integer quantum numbers areintroduced in the theory of thehydrogen atom.

Wolfgang Pauli (1900-1958)formulates the exclusion principle forthe electron, accounting for a numberof chemical properties in atoms andmolecules.

Planck devises a new derivation ofthermodynamic formulas forBoltzmann gases using theformulations,

z = exp(-Îľ/kT), Z = zN / N!


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Ernst Ising (1900-), following theinvestigations of Lenz, publishes apaper dealing with magnetic modelsvia dipolar atomic interactions.

1926

Born introduces into quantummechanics his probabilityinterpretation of interactions.

Enrico Fermi (1901-1954) derives thestatistical properties of gases whichobey the Pauli exclusion principle.

Erwin Rudolf Josef AlexanderSchrĂ¶dinger (1887-1961)developes a second formulation ofquantum theory in terms of wavemechanics independently.

Paul Adrien Maurice Dirac(1902-1984) relates the symmetry ofquantum mechanical wave functionsto the statistics of Bose, Einsteinand Fermi. He also derives the Planckdistribution from first principles.

Eddington's The InternalConstitution of the Stars, relating theradiation pressure of stars to theirluminosity.

Fowler shows that some of theproperties of white dwarf stars couldbe accounted for by treating them as(Fermi) quantum degenerate gases,being an early example of quantumstatistics explaining the properties oflarge macroscopic objects.

Robert Hutchings Goddard launchesthe first rocket, using liquid fuel andreaching a height of 184 feet and 60miles per hour.

Paul Dirac


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1927

John von Neumann (1903-1957)formulates a fully quantummechanical generalization ofstatistical mechanics.

Bohr pronounces his notion ofcomplimentarity in quantum theory.

Heisenberg formulates theuncertainty principle of quantummechanics.

Dirac and Pauli independentlypropose to model metals withmolecules obeying Fermi-Diracstatistics.

Pauli explains the paramagneticsusceptibility of metals using electronspin and the exclusion principle.

Willem Hendrik Keesom (1876-1956)and M Wolfke find discontinuities inseveral properties of helium at verylow temperatures and suggest that itmay be due to a phase change,calling them helium I and II.

Walter Heitler (1904-) and FritzLondon (1900-1954) applyHeisenberg's resonance theory tothe covalent molecular bond betweentwo hydrogen atoms, showingstability to a function of electronspins, and arguing against thestability of such helium bonds.

1928

Sommerfeld treats electrons inmetals as a degenerate Fermi gasusing the new techniques of quantumtheory.

Dirac comes up with a relativisticquantum mechanical wave equation


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for the electron.

Felix Bloch (1905-) suggests a theoryof metals based on electrons layeredperiodic positive potentials which cansustain small displacements whichlead to resistance via scattering ofelectrons by the lattice vibrations.

John Clarke Slater (1900-1976) is thefirst to study the quantum mechanicaltreatment of the molecular formationof rare gases (helium).

Linus Pauling (1901-) applies theHeitler-London treatment to chemicalbonds.

1929

Edmund Clifton Stoner (1899-1968),using (special) relativistic formulasfor electron energies, suggests thatbeyond a certain density in stars theoutward degenerate gas pressurewould no longer sustain itself againstthe inward gravitational attraction(though he did not speculate aboutwhat would then happen).

Slater formulates a multi-electronwave function which can generallysatisfy the Pauli exclusion principle.

John vonNeumann1930

Discovery of the lambda point ofhelium at which it becomes asuperfluid (so-named in 1941) at2.2Â°K.

1931

George David Birkhoff (1884-1944)proves the general ergodic theoreom.

Pauling publishes his work onchemical bonds, proving the stabilityof such bonds.


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1932

Aleksandr Yakovlevich Khinchin(1894-1959), in work through 1934,founds the modern study ofstationary random processes.

1933

Walther Meissner (1882-1974) and ROchsenfeld report that metals cooledbelow their superconductingtemperatures in a magnetic fieldcompletely expell all lines ofmagnetic induction, becoming aperfect diamagnet.

1934

William Lawrence Bragg (1890-1971)and Williams formulates an Isingmodel for paramagnetic toferromagnetic transitions.

Cornelius Jacobus Gorter (1907-1980)and Hendrik Bruygt Gerhard Casimir(1909-) form an analysis of theexpulsion of magnetic fields insuperconducting metals in amagnetic field.

1935

William Francis Giauque achieves atemperature of only 0.1Â°K forhelium using a magnetic trap to slowthe motion of the molecules.

Lev Davidovich Landau(1908-1968) publishes hisphenomenological mean-fieldtreatment for phase transitions.

Subrahmanyan Chandrasekhar(1910-1995) derives the maximummass formula for a degenerate Fermigas.

Fritz Wolfgang London (1900-1954)and brother Heinz London work on asuperconductivity theory ofmacroscopic objects using classicalelectrodynamical theory and some

Lev Landau


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additional assumptions.

Hans Bethe (1906-) improves onBragg-Williams theory by addingshort-range atomic interactions.

Edward Armand Guggenhaim (1901-)develops a theory of liquid solutionsusing nearest-neighbor rules, intowhat is now callod the "quasi-chemical" (QC) method.

1936

Joseph Edward Mayer (1904-) (seelinks) and Sally F Harrison (1913-),along with Maria Goeppert-Mayer(1906-1972), initiate the moderntheory of gas condensation, in workthrough 1938, by use of "clusterintegrals" representing theinteractions of many molecules tofind the virial coefficients ofintermolecular forces.

1937

Peter Leonidovich Kapitza (1894-?)determines that helium II has aviscosity of about 1500 times smallerthan helium I and terms thephenomena "superfluidity." At almostthe same time, John Frank Allen(1908-) and A D Miscner discover thesame effect independently(publishing 19 days later).

John Edward Leonard-Jones(1894-1954) and A F Devonshireformulate (through '39) the "6-12potential" for intermolecular forces.

1938

Claude Elwood Shannon (1916-)publishes A Symbolic Analysis ofRelay and Switching Circuits,instigating the study of informationtheory and giving a systematic way ofmathematically treating noise.

Claude Shannon


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London's theoretical work on liquidhelium and Bose-Einsteincondensation.

1939

W Conyer Herring calculates bulkproperties of materials from quantumprinciples, specifically explaining howberyllium acts as a metal.

1940

Fowler and Guggenheim extend theQC method, applying it to modelswhich take into account longer-rangeinteractions.

1942

Lars Onsager (1903-1976) (also seelinks) gives his solution to thetwo-dimensional Lenz-Ising model,showing that a phase transition willoccur. "[I]t is the first exact solutionof a nontrivial problem in statisticalmechanics, in which interparticleforces are taken into account withoutapproximation" (SG Brush).

1944

Evgenni Mikhailovich Lifshitz(1915-1985) shows that "second-sound" waves in superfluids can bedetected as temperature deviations.The effect is experimentallyconfirmed shortly there after by VPeshkov.

1946

Nikolai Nikolaevich Bogolyubov(1909-) writes his Problems ofDynamical Theory in StatisticalPhysics. He works on a generalizationof the Boltzmann equation, using thetime-reversal invariant Liouvilleequation, further clarifying theinternal structure of statisticalmechanics.

Khinchin refines Boltzmann'stheorem to read that, as a function ofthe size of an ensembles, the timeaverage of a system becomes


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arbitrary close to the canonicalaverage.

Richard A Ogg, Jr suggests that pairsof electrons behave as bosons, andthat superconductivity may bethought of as a Bose-Einsteincondensate. (The idea is ignored untilabout 1954.)

1948

Shannon's major publication oninformation theory and symboliclogic, A Mathematical Theory ofCommunication.

1950

Herbert FrĂ¶lich (1905-) suggeststhat phonon interactions betweenelectrons may be the basis of anexplanation of superconductivity,giving one of the first uses ofquantum field theory to statisticalmechanics.

1953

Richard Phillips Feynman(1918-1988) begins his work on thetheory of superconducting heliumusing his path-integral approach,further clarifying how previoustheoretical attempts have workedand/or failed.

1955

Erwin Wilhelm Mueller's (1911-1977)field ion microscope is the firstinstrument to allow imaging ofindividual atoms.

W Noll proves that by taking theappropriate phase averages, anymolecular system modelled bystatistical mechanics can be shown tosatisfy exactly the equivalent fieldequations for a continuous material,thus theoretically showing theequivalence of the two approaches.


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1956

Leon Cooper (1930-), John Bardeen(1908-) and John Robert Schrieffer(1931-) form a many-electron theoryof superconduction which gives goodagreement with experiment andproduces the Meissner effect.

1957

Khinchin's book, MathematicalFoundations of Information Theory.

Berni Julian Alder (1925-) andThomas Everett Wainwright (1927-)computationally discover thehard-sphere phase transition.

1961

George Allen Baker, Jr (1932-) founda method of determining thesingularities at the critical point viaseries expansions of Lenz-Isingmodels.

1965Benjamin Widom 's (1927-) work onsurface tension theory using amodified van der Waals theory.

1968Alder and Wainwright discover vortexdiffusion in liquids.

1971

Kenneth Wilson (1936-), extendingearlier work by Leo Kadanoff (in1966), applies the technique of therenormalization group to study ofscaling laws for phase transitiontheory.

1972

Michel Ellis Fisher (1931-) andWidom show that the Lenz-Isingmodel generalized to arbitrarydimensions display a continuoustransition between classical andnon-classical laws, where correlationlengths tend toward infinity at criticalpoints.

1980Heinrich Rohrer and Gerd Binnigdevelop the scanning tunnellingmicroscope, allowing for imaging of


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atoms embedded on surfaces.

Sources: Brush, Stephen G, Statistical Physics and the AtomicTheory of Matter From Boyle and Newton to Landauand Onsager (out of print)Bunch, Bryan & Hellemans, Alexander, The Timetablesof ScienceEisberg, R and Resnick, R, Quantum Physics, 2nd ed,1985Flamm, Dieter, "History and outlook of statisticalphysics," physics/9803005, 4 March, 1998Flamm, Dieter, "Ludwig Boltzmann - A Pioneer ofModern Physics," physics/9710007, 7 October, 1997Kuhn, Thomas S, Black-Body Theory and the QuantumDiscontinuity, 1894-1912Mendoza, E, "A Sketch for a History of Earlythermodynamics," Physics Today, February 1961, p 32Mendoza, E, "A Sketch for a History of the KineticTheory of Gases," Physics Today, March 1961Mendelssohn, K, The Quest for Absolute Zero (out ofprint)Moore, Walter, SchrĂ¶dinger: Life and ThoughtTruesdell, C, Essays in the History of Mechanics (out ofprint)

And the great MacTutor History of MathematicsArchive

Links: The Pneumatics of Hero of AlexandriaPaul Charlesworth's History of Science pagesChris Hillman's Entropy in the Physical SciencesBiographies of chemists and some physicists availableat the History of Chemistry pageAbout Temperature by Project SkymathFahrenheit's Paper of 1724The Origin of the Celsius Temperature ScaleWave Mechanics: Louis de Broglie

The Lars Onsager ArchiveRegister of Joseph Mayer's Papers


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Notes:Would like to get into more history of probability theory as it applied tothese histories.Need to read more works by Mr Truesdell (the above book is great).Filling out more pre-17th century material would really enhance theperspective of the timeline.Certain mathematico-conceptual issues eventually have to be dealtwith.

If there's anything that you feel should be address, or addressed morefully, or if there are references which you'd like to suggest I look into,please feel free to email the author at [email protected].


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sketching the history of statistical mechanics and

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