maxwell's demon: implications for evolution and biogenesis
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Maxwell's Demon: Implications for Evolution and Biogenesis Avshalom C. Elitzur Iyar, The Israeli Institute for Advanced Research. Copyleft 2010. The Relevance of Thermodynamics to Life Sciences . Thermodynamics is a discipline that studies energy, entropy, and information. - PowerPoint PPT PresentationTRANSCRIPT
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Maxwell's Demon: Implications for Evolution and Biogenesis
Avshalom C. ElitzurIyar, The Israeli Institute for Advanced Research
Copyleft 2010
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The Relevance of Thermodynamicsto Life Sciences
1. Thermodynamics is a discipline that studies energy, entropy, and information
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Brillouin’s Information:Information=(Initial Uncertainty)–(Final Uncertainty)
For several equally possible states, P0
With information reducing the possible states to P1:
Ideally, for P1=1:
)ln(lnln 101
0 PPKPPKI
0I
0ln PKI
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Shannon’s Information:Uncertainty = Entropy
Boltzmann’s Entropy
For all states being equiprobable:
Otherwise:
Information of one English letter:
For a string of G letters:
w
ij
ppkS 11 ln
27
111 ln
j
ppki
mj
ij
ppGkiGI 11 ln
WkS ln
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The Relevance of Thermodynamicsto Life Sciences
1. Thermodynamics is a discipline that studies energy, entropy, and information
2. Its jurisdiction is ubiquitous, regardless of the system’s chemical composition or type of energy
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Whence the entropy differencebetween animate and inanimate systems ?
The Common Textbook Answer:
“Living organisms are open systems”
?
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Open Systems:
Rocks
Chairs
Blackboards
Trash cans (!)
etc.
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The Thesis:
Adaptation = Information
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Maxwell’s Demon
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Attempts at Exorcizing
1. Kelvin: The devil is alive2. Von Smoluchowski: It’s intelligent3. Szilard, Brillouin: It uses information4. Bennett & Landauer: It erases information
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Information and Energy
Information Costs Energyergo
Information can Save Energy
With information, you can do work with less energy, applied at the right time and/or place
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“Less energy, at the right time/place”
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“Less energy, at the right time/place”:Comparison between two methods of kill
Considerable mechanical energy: Crushing the entire prey’s body
Minute chemical energy: Neurotoxin (cobrotoxin) moleculesreach the synapses with enormous precision
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Ek Et
Ec EtEe
The Demon Vs. the Living Organism: The Analogy
1) Life increases energy’s efficiency, up the thermodynamic scale2) It does that with the aid of information
Ec + Ee Ec'> Ec
Ec + Ee Ek
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The Demon Vs. the Living Organism: The Disanalogy 1) The real environment is never completely disordered but complex 2) The organism does not create order but complexity
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Ordered, Random, ComplexMeasures of Orderliness
1. Divergence from equiprobability (Gatlin) (Are there any digits in the sequence that are more common?)
2. Divergence from independence (Gatlin) (Is there any dependence between the digits?)
3. Redundancy (Chaitin) (Can the sequence be compressed into any shorter algorithm?)
a. 3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333
b. 1860271194945955774038867706591873856869843786230090655440136901425331081581505348840600451256617983
c. 0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789
d. 6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911374
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215
Sequence d is complex
Sequence d is highly informative
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Bennett’s Measure of Complexity
Given the shortest algorithm, how much computation is required to produce the sequence from it?
And conversely:
How much computation is required to encode a sequence into its shortest algorithm?
High order
complexity
Low order
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The Ski-Lift Pathway: Thermodynamically Unique, Biologically Ubiquitous
Goren Gordon & Avshalom C. Elitzur
High Order
Low Order
RequiresEnergy
Spontaneous
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Desired State
High Order
Low Order
RequiresEnergy
Spontaneous
Step 1:Use Ski-Lift,
get to the top
How do you get to some desired state?
Initial State
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High Order
Low Order
RequiresEnergy
Spontaneous
Step 1:Use Ski-Lift,
get to the top
How do you get to some desired state?
Desired State Initial State
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High Order
Low Order
RequiresEnergy
Spontaneous
Step 2:Ski down
Step 1:Use Ski-Lift,
get to the top
How do you get to some desired state?
Desired State Initial State
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The Ski-Lift Conjecture (Gordon & Elitzur, 2009):
Life approaches complexity “from above,” i.e., from the high-
order state, and not “from below,” from the low-order state.
Though the former route seems to require more energy, the latter
requires immeasurable information, hence unrealistic energy.
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Dynamical evolution of complex states
How to reach a complex state?
1. Direct path
1. Probabilistic
2. Deterministic
2. Ski-lift theorem
Initial state Final state
Entro
py
Direct path
Ski-lift
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Perform a transformation on the initial state to arrive at the final state
Ti!f (???)
Initial state unknown
For each transformation only one initial state transforms to final state
Hilbert Space
Initial stateFinal state
Direct Path
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Perform a transformation on the initial state to arrive at the final state
Ti!f (???)
Initial state unknown
For each transformation only one initial state transforms to final state
Perform transformation once
Energy cost:E=
Probability of success:P=1/Ni
=e-S(i)¿ 1
Hilbert Space
Initial stateFinal state
Direct Path: Probabilistic
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Perform a transformation on the initial state to arrive at the final state
Ti!f (???)
Initial state unknown
For each transformation only one initial state transforms to final state
Repeat transformation until finalstate is reached
Probability of success:P=1
Average energy cost:E= eS(i)À 1
Direct Path: Deterministic
Hilbert Space
Initial stateFinal state
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Perform a transformation on the initial state to arrive at the final state
Ti!f If one has information about initial state
Ii=S(i)And information about final state (environment)
If=S(f)
Then can perform the right transformation once
Probability of success:P=1
Energy cost:E=
Information required:I=S(i)+S(f)
Direct Path: Information
Hilbert Space
Initial stateFinal state
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Two stages path:
Stage 1: Increase orderS-i! order
Ends with a specific, known stateProbability of success: P1=1Energy cost: E1=S(i)
Ski-lift Path
Hilbert Space
Initial stateFinal state
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Two stages path:
Stage 1: Increase orderS-i! order
Ends with a specific, known stateProbability of success: P1=1Energy cost: E1=S(i)
Stage 2: Controlled transformationTorder!f
Ends with the specific, final stateProbability of success: P2=1Energy cost: E2=
Ski-lift Path
Hilbert Space
Initial stateFinal state
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Requires information on final state (environment), in order to apply the right transformation on ordered-state
Probability of success: P=1
Energy cost: Eski-lift=S(i)+
Information required:I=S(f)
Hilbert Space
Initial stateFinal state
Ski-lift Path: Information
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Comparison between pathsDirect Path
1. Probabilistic1. Low probability2. Low energy
2. Deterministic:1. High probability2. High energy
3. Information:1. Requires much information2. Low energy
Ski-lift• Deterministic• Controlled• Reproducible• Costs low energy• Requires only environmental information
Ski-lift uses ordered-state and environmental information to obtain controllability and reproducibility
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How does Complexity Emerge?And How is it Maintained?
Information/ComplexityOrder Disorder
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Bennett’s Measure of Complexity
Given the shortest algorithm, how much computation is required to produce the sequence from it?
And conversely:
How much computation is required to encode a sequence into its shortest algorithm?
High order
complexity
Low order
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Biological examples
• Cell formation• Apoptosis• Embryonic development• Ecological development
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The Morphotropic State as the Cellular Progenitor of Complexity
Minsky A, Shimoni E, Frenkiel-Krispin D. (2002) “Stress, order and survival.” Nat. Rev. Mol. Cell Biol. Jan;3(1):50-60.
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Order as the Ecological Progenitor of Complexity
Maintaining the complexity of civilization necessitateshuge reservoirs of order
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Schrödinger’s “What is life?” revisited
Hilbert Space
High orderRedundancy
High entropyHigh informationHigh complexity
(specific environment)
Requires energy
Requires information
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BIBLIOGRAPHY
1. Leff, H. S., & Rex, A. F. (2003) Maxwell’s Demon 2: Entropy, Classical and Quantum Information, Computing. Bristol: Institute of Physics Publishing.
2. Dill, K.A. , & Bromberg, S. (2003) Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology. New York: Garland Science.
3. Di Cera, E., Ed. (2000) Thermodynamics in Biology” Oxford: Oxford University Press.
4. Gordon, G., & Elitzur, A. C. (2008) The Ski-Lift Pathway: Thermodynamically unique, biologically ubiquitous. http://www.a-c-elitzur.co.il/site/siteArticle.asp?ar=214