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Stochastic Thermodynamics
1. Prelude & Brief History of Fluctuation theorems
2. Thermodynamics & Jarzynski/Crooks FT
3. Experiments & Applications
4. Stochastic thermodynamics & FTs
5. Detailed balance & Fluctuation-dissipation theorem
6. Information thermodynamics
7. Summary $ Outlook
Nonequilibrium statistical physics & active matter systems IOP, CAS, Beijing (Aug. 11-13, 2016)
Hyunggyu Park 박 형 규 朴 炯 奎
Summary of Part I
Jarzynski equality
Crooks relation
: time-reverse path
Stochastic thermodynamics
Stochastic thermodynamics
Microscopic deterministic dynamics
Stochastic thermodynamics
Microscopic deterministic dynamics
Stochastic thermodynamics
Microscopic deterministic dynamics
Stochastic thermodynamics
Microscopic deterministic dynamics
Stochastic dynamics
Stochastic thermodynamics
Microscopic deterministic dynamics
Stochastic dynamics
Stochastic thermodynamics
Microscopic deterministic dynamics
Stochastic dynamics
Stochastic thermodynamics
Microscopic deterministic dynamics
Stochastic dynamics
Stochastic thermodynamics
Microscopic deterministic dynamics
Macroscopic thermodynamics
Stochastic dynamics
Stochastic thermodynamics
Microscopic deterministic dynamics
Macroscopic thermodynamics
Stochastic dynamics
Stochastic thermodynamics
Microscopic deterministic dynamics
Macroscopic thermodynamics
Stochastic dynamics
Stochastic thermodynamics
Microscopic deterministic dynamics
Macroscopic thermodynamics
Stochastic dynamics
Stochastic thermodynamics
Microscopic deterministic dynamics
Macroscopic thermodynamics
Stochastic dynamics
Stochastic thermodynamics
Microscopic deterministic dynamics
Macroscopic thermodynamics
Stochastic dynamics
Stochastic thermodynamics
Microscopic deterministic dynamics
Macroscopic thermodynamics
Stochastic dynamics
Stochastic thermodynamics
Microscopic deterministic dynamics
Macroscopic thermodynamics
Stochastic dynamics
Stochastic thermodynamics
Microscopic deterministic dynamics
Macroscopic thermodynamics
Stochastic dynamics
Stochastic thermodynamics
Equilibrium
Stochastic thermodynamics
Equilibrium
Stochastic thermodynamics
state space
Equilibrium
Stochastic thermodynamics
state space
Equilibrium
Stochastic thermodynamics
state space
Equilibrium
Stochastic thermodynamics
state space
Equilibrium
Stochastic thermodynamics
state space
Equilibrium
Stochastic thermodynamics
state space
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
state space
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
System
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
System
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
System
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
System
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
System
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
System
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
System
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
System
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
System
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
System
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
System
Equilibrium Nonequilibrium Process
Stochastic thermodynamics
trajectory
System
Langevin (stochastic) dynamics
Langevin (stochastic) dynamics
Langevin (stochastic) dynamics
System
Langevin (stochastic) dynamics
state space
trajectory
System
Langevin (stochastic) dynamics
state space
trajectory
System
Langevin (stochastic) dynamics
state space
trajectory
System
Langevin (stochastic) dynamics
state space
trajectory
System
Langevin (stochastic) dynamics
state space
trajectory
System
Langevin (stochastic) dynamics
state space
trajectory
System
Langevin (stochastic) dynamics
state space
trajectory
System
Langevin (stochastic) dynamics
state space
trajectory
System
Langevin (stochastic) dynamics
state space
trajectory
System
Langevin (stochastic) dynamics
state space
trajectory
System
Langevin (stochastic) dynamics
state space
trajectory
System
Langevin (stochastic) dynamics
state space
trajectory
System
Langevin (stochastic) dynamics
state space
trajectory
System
Langevin (stochastic) dynamics
state space
trajectory
System
Langevin (stochastic) dynamics
state space
trajectory
System
Langevin (stochastic) dynamics
state space
trajectory
System
Langevin (stochastic) dynamics
state space
trajectory
System
Stochastic process, Irreversibility & Total entropy production
Stochastic process, Irreversibility & Total entropy productionstate space
trajectory
Stochastic process, Irreversibility & Total entropy productionstate space
trajectory
Stochastic process, Irreversibility & Total entropy productionstate space
trajectory
time-rev
Stochastic process, Irreversibility & Total entropy productionstate space
trajectory
time-rev
Stochastic process, Irreversibility & Total entropy productionstate space
trajectory
time-rev
Stochastic process, Irreversibility & Total entropy productionstate space
trajectory
time-rev
Stochastic process, Irreversibility & Total entropy productionstate space
trajectory
time-rev
Stochastic process, Irreversibility & Total entropy productionstate space
trajectory
time-rev
Stochastic process, Irreversibility & Total entropy productionstate space
trajectory
time-rev
Total entropy production and its components
Total entropy production and its components
Total entropy production and its components
Total entropy production and its components
Total entropy production and its components
Total entropy production and its components
Total entropy production and its components
Total entropy production and its components
System
Total entropy production and its components
System
Total entropy production and its components
System
Total entropy production and its components
System
Total entropy production and its components
System
Total entropy production and its components
System
Total entropy production and its components
System
Total entropy production and its components
System
Total entropy production and its components
System
Total entropy production and its components
System
Total entropy production and its components
System
Total entropy production and its components
System
Total entropy production and its components
System
Total entropy production and its components
System
Total entropy production and its components
System
Total entropy production and its components
System
Total entropy production and its components
Total entropy production and its components
Total entropy production and its components
Total entropy production and its components
Total entropy production and its components
Total entropy production and its components
Total entropy production and its components
Total entropy production and its components
Total entropy production and its components
Total entropy production and its components
Total entropy production and its components
Total entropy production and its components
Probability theory viewpoint
on Fluctuation theorems
Seifert, PRL 95, 040602 (2005) Esposito/VdBroeck, PRL 104, 090601 (2010)
Fluctuation theorems System
Fluctuation theorems
Integral fluctuation theorems
System
Fluctuation theorems
Fluctuation theorems
Integral fluctuation theorems
Fluctuation theorems
Integral fluctuation theorems
Fluctuation theorems
Integral fluctuation theorems
Thermodynamic 2nd laws
Fluctuation theorems
Integral fluctuation theorems
Detailed fluctuation theorems
Thermodynamic 2nd laws
Fluctuation theorems
Integral fluctuation theorems
Detailed fluctuation theorems
Thermodynamic 2nd laws
Probability theory
Probability theory
• Consider two normalized PDF’s :
Probability theory
• Consider two normalized PDF’s : state space
trajectory
Probability theory
• Consider two normalized PDF’s : state space
trajectory
Probability theory
• Consider two normalized PDF’s : state space
trajectory
Probability theory
• Consider two normalized PDF’s : state space
trajectory
• Define “relative entropy”
Probability theory
• Consider two normalized PDF’s : state space
trajectory
• Define “relative entropy”
Probability theory
• Consider two normalized PDF’s : state space
trajectory
• Define “relative entropy”
Probability theory
• Consider two normalized PDF’s : state space
trajectory
• Define “relative entropy”
Probability theory
• Consider two normalized PDF’s : state space
trajectory
• Define “relative entropy”
Integral fluctuation theorem
Probability theory
• Consider two normalized PDF’s : state space
trajectory
• Define “relative entropy”
Integral fluctuation theorem
(exact for any finite-time trajectory)
Probability theory
• Consider two normalized PDF’s : state space
trajectory
• Define “relative entropy”
Integral fluctuation theorem
(exact for any finite-time trajectory)
Probability theory
• Consider two normalized PDF’s : state space
trajectory
• Define “relative entropy”
Integral fluctuation theorem
(exact for any finite-time trajectory)
Probability theory
• Consider the mapping :
Probability theory
• Consider the mapping :
• Require
Probability theory
• Consider the mapping :
• Require reverse path
Probability theory
• Consider the mapping :
• Require reverse path
Probability theory
• Consider the mapping :
• Require reverse path
Probability theory
• Consider the mapping :
• Require reverse path
Probability theory
• Consider the mapping :
• Require
Detailed fluctuation theorem
reverse path
Probability theory
• Consider the mapping :
• Require
Detailed fluctuation theorem
reverse path
(exact for any finite t)
Probability theory
• Consider the mapping :
• Require
Detailed fluctuation theorem
reverse path
(exact for any finite t)
Probability theory
• Consider the mapping :
• Require
Detailed fluctuation theorem
reverse path
(exact for any finite t)
Probability theory
• Consider the mapping :
• Require
Detailed fluctuation theorem
reverse path
(exact for any finite t)
Dynamic processes & Path probability ratio
Dynamic processes & Path probability ratio
Dynamic processes & Path probability ratio
Dynamic processes & Path probability ratio
Dynamic processes & Path probability ratio
Dynamic processes & Path probability ratio
Dynamic processes & Path probability ratio
Dynamic processes & Path probability ratio
: time-reverse path
Dynamic processes & Path probability ratio
: time-reverse path
Markovian jump dynamics
Markovian jump dynamics
Markovian jump dynamics
Markovian jump dynamics
Markovian jump dynamics
Markovian jump dynamics
Markovian jump dynamics
Markovian jump dynamics
Markovian jump dynamics
Markovian jump dynamics
Markovian jump dynamics
Markovian jump dynamics
Markovian jump dynamics
Markovian jump dynamics s R
Markovian jump dynamics s R
Reservoir entropy change Schnakenberg/Hinrichsen/Park
Reservoir entropy change Schnakenberg/Hinrichsen/Park
Reservoir entropy change Schnakenberg/Hinrichsen/Park
Reservoir entropy change Schnakenberg/Hinrichsen/Park
Reservoir entropy change Schnakenberg/Hinrichsen/Park
Reservoir entropy change Schnakenberg/Hinrichsen/Park
Reservoir entropy change Schnakenberg/Hinrichsen/Park
Reservoir entropy change Schnakenberg/Hinrichsen/Park
Reservoir entropy change Schnakenberg/Hinrichsen/Park
Reservoir entropy change Schnakenberg/Hinrichsen/Park
Reservoir entropy change Schnakenberg/Hinrichsen/Park
Reservoir entropy change Schnakenberg/Hinrichsen/Park
Reservoir entropy change Schnakenberg/Hinrichsen/Park
Reservoir entropy change Schnakenberg/Hinrichsen/Park
Langevin dynamics
Langevin dynamics
Langevin dynamics
Langevin dynamics
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Discretization scheme for a path integral
Langevin dynamics
Langevin dynamics
Langevin dynamics
Langevin dynamics
: time-reverse path
Langevin dynamics
: time-reverse path
Langevin dynamics
: time-reverse path
Langevin dynamics
: time-reverse path
Langevin dynamics
: time-reverse path
Langevin dynamics
: time-reverse path
Langevin dynamics
: time-reverse path
Fluctuation theorems
Fluctuation theorems
reverse path
Fluctuation theorems
reverse pathIrreversibility (total entropy production)
Fluctuation theorems
reverse pathIrreversibility (total entropy production)
Fluctuation theorems
reverse pathIrreversibility (total entropy production)
Fluctuation theorems
reverse pathIrreversibility (total entropy production)
Fluctuation theorems
reverse pathIrreversibility (total entropy production)
Fluctuation theorems
reverse pathIrreversibility (total entropy production)
Fluctuation theorems
reverse pathIrreversibility (total entropy production)
Fluctuation theorems
reverse pathIrreversibility (total entropy production)
Fluctuation theorems
reverse pathWork free-energy relation (dissipated work)
Fluctuation theorems
reverse pathWork free-energy relation (dissipated work)
Fluctuation theorems
reverse pathWork free-energy relation (dissipated work)
Fluctuation theorems
reverse pathWork free-energy relation (dissipated work)
Fluctuation theorems
reverse pathWork free-energy relation (dissipated work)
Fluctuation theorems
reverse pathWork free-energy relation (dissipated work)
Fluctuation theorems
reverse pathWork free-energy relation (dissipated work)
Fluctuation theorems
reverse pathWork free-energy relation (dissipated work)
Fluctuation theorems
reverse pathWork free-energy relation (dissipated work)
Fluctuation theorems
reverse pathWork free-energy relation (dissipated work)
Fluctuation theorems
reverse pathWork free-energy relation (dissipated work)
Fluctuation theorems
reverse pathWork free-energy relation (dissipated work)
Fluctuation theorems
reverse pathWork free-energy relation (dissipated work)
Fluctuation theorems
reverse pathWork free-energy relation (dissipated work)
Fluctuation theorems
reverse pathWork free-energy relation (dissipated work)
Fluctuation theorems
reverse pathHouse-keeping & Excess entropy production
Fluctuation theorems
reverse pathHouse-keeping & Excess entropy production
Fluctuation theorems
reverse pathHouse-keeping & Excess entropy production
Fluctuation theorems
reverse pathHouse-keeping & Excess entropy production
NEQ steady state (NESS) for fixed
Fluctuation theorems
reverse pathHouse-keeping & Excess entropy production
NEQ steady state (NESS) for fixed
Fluctuation theorems
reverse pathHouse-keeping & Excess entropy production
NEQ steady state (NESS) for fixed
Fluctuation theorems
reverse pathHouse-keeping & Excess entropy production
NEQ steady state (NESS) for fixed
Fluctuation theorems
reverse pathHouse-keeping & Excess entropy production
NEQ steady state (NESS) for fixed
Fluctuation theorems
reverse pathHouse-keeping & Excess entropy production
NEQ steady state (NESS) for fixed
Fluctuation theorems
reverse pathHouse-keeping & Excess entropy production
NEQ steady state (NESS) for fixed
Fluctuation theorems
reverse pathHouse-keeping & Excess entropy production
NEQ steady state (NESS) for fixed
Fluctuation theorems
reverse pathHouse-keeping & Excess entropy production
NEQ steady state (NESS) for fixed
Fluctuation theorems
reverse pathHouse-keeping & Excess entropy production
NEQ steady state (NESS) for fixed