Fluctuation theorem: A critical review

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.