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Fluctuation theorem: A critical review.

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The fluctuation theorem for entropy production has limitations in describing non-equilibrium systems using stochastic thermodynamics, especially for jump Markov processes and stationary diffusion systems.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Physical Chemistry

Background:

  • The fluctuation theorem for entropy production provides insights into non-equilibrium systems.
  • Stochastic thermodynamics extends classical thermodynamics to microscopic processes.
  • Understanding the applicability of these theorems is crucial for analyzing complex systems.

Purpose of the Study:

  • To revisit the fluctuation theorem for entropy production within the framework of stochastic processes.
  • To analyze the applicability of the fluctuation theorem to physico-chemical systems.
  • To identify limitations of stochastic thermodynamics in describing non-equilibrium states.

Main Methods:

  • Analysis of fluctuation theorem in the context of stochastic processes.
  • Investigation of jump Markov processes and diffusion processes.
  • Evaluation of thermodynamic properties of individual processes in non-equilibrium systems.

Main Results:

  • Unexpected limitations were found for jump Markov processes, hindering accurate description of non-equilibrium systems.
  • Stochastic thermodynamics faces challenges in characterizing individual processes within these systems.
  • For one-variable diffusion processes, the fluctuation theorem for entropy production is irrelevant at the stationary state.

Conclusions:

  • The fluctuation theorem and resulting stochastic thermodynamics have specific limitations, particularly for certain types of stochastic processes.
  • Accurate thermodynamic description of non-equilibrium systems requires careful consideration of the underlying stochastic dynamics.
  • Further research is needed to refine stochastic thermodynamics for broader applicability.