Stochastic thermodynamics: Principles and perspectives

TL;DR

This paper reviews stochastic thermodynamics, a framework for analyzing small, out-of-equilibrium systems, highlighting key principles, exact relations, and potential extensions to stochastic field equations.

Contribution

It provides a comprehensive overview of the principles and recent developments in stochastic thermodynamics, including fluctuation theorems and their applications to various systems.

Findings

Derivation of fluctuation theorems for entropy production

Application of stochastic thermodynamics to biochemical systems

Extension of principles to stochastic field equations like KPZ

Abstract

Stochastic thermodynamics provides a framework for describing small systems like colloids or biomolecules driven out of equilibrium but still in contact with a heat bath. Both, a first-law like energy balance involving exchanged heat and entropy production entering refinements of the second law can consistently be defined along single stochastic trajectories. Various exact relations involving the distribution of such quantities like integral and detailed fluctuation theorems for total entropy production and the Jarzynski relation follow from such an approach based on Langevin dynamics. Analogues of these relations can be proven for any system obeying a stochastic master equation like, in particular, (bio)chemically driven enzyms or whole reaction networks. The perspective of investigating such relations for stochastic field equations like the Kardar-Parisi-Zhang equation is sketched as well.