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Published on: December 4, 2017
Nonadiabatic entropy production for non-Markov dynamics.
1Centro Atómico Bariloche and Instituto Balseiro, 8400 San Carlos de Bariloche, Argentina. reinaldo.garcia@cab.cnea.gov.ar
Summary
We extend nonadiabatic entropy production to non-Markovian dynamics and introduce a stability criterion. Stable non-Markovian systems satisfy fluctuation theorems and the second law of thermodynamics.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Non-equilibrium Physics
Background:
- The definition of nonadiabatic entropy production was previously limited to Markovian systems.
- Understanding entropy production in non-Markovian systems is crucial for non-equilibrium thermodynamics.
Purpose of the Study:
- To extend the definition of nonadiabatic entropy production to arbitrary non-Markov ergodic dynamics.
- To introduce and analyze a notion of stability for non-Markovian systems.
- To investigate the validity of fluctuation theorems and the generalized fluctuation-dissipation relation in non-Markovian systems.
Main Methods:
- Extension of existing theoretical frameworks for entropy production.
- Introduction of a novel stability criterion for non-Markovian dynamics.
- Analysis of integral fluctuation theorems and generalized fluctuation-dissipation relations.
Main Results:
- Nonadiabatic entropy production is extended to non-Markov ergodic dynamics.
- A stability criterion is introduced, characterizing non-Markovianity.
- Stable non-Markovian systems satisfy an integral fluctuation theorem and the second law of thermodynamics.
- The generalized fluctuation-dissipation relation holds for ergodic and stable systems, not necessarily Markovian ones.
- Violation of the stability criterion in ergodic non-Markovian systems leads to violations of the fluctuation theorem and generalized fluctuation-dissipation relation.
Conclusions:
- Stability is a necessary condition for fluctuation theorems and the generalized fluctuation-dissipation relation in non-Markovian systems.
- The introduced stability criterion explains the elusiveness of the generalized fluctuation-dissipation relation in non-Markov systems.
- This work provides a foundation for thermodynamics of non-Markovian systems far from equilibrium.
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