Thermodynamic Langevin Equations

TL;DR

This paper derives thermodynamic Langevin equations for small systems, linking fluctuations, entropy, and nonequilibrium conditions, and compares macroscopic and microscopic descriptions in stochastic thermodynamics.

Contribution

It introduces exact nonlinear thermodynamic Langevin equations based on entropic forces, connecting stochastic processes with thermodynamic fluctuations in small systems.

Findings

TLEs incorporate entropic forces and describe thermodynamic fluctuations.

Currents in the canonical ensemble lead to nonequilibrium heat transfer bounds.

Differences between macroscopic TLEs and microscopic stochastic thermodynamics are highlighted.

Abstract

The physical significance of the stochastic processes associated to the generalized Gibbs ensembles is scrutinized here with special attention to the thermodynamic fluctuations of small systems. The contact with the environment produces an interaction entropy, which controls the distribution of fluctuations and allows writing the generalized Gibbs ensembles for macrostates in potential form. This naturally yields exact nonlinear thermodynamic Langevin equations (TLEs) for such variables, with drift expressed in terms of entropic forces. The analysis of the canonical ensemble for an ideal monoatomic gas and the related TLEs show that introducing currents leads to nonequilibrium heat transfer conditions with interesting bounds on entropy production but with no obvious thermodynamic limit. For a colloidal particle under constant force, the TLEs for macroscopic variables are different from those for the microscopic position, typically used in the so-called stochastic thermodynamics; while TLEs are consistent with the fundamental equation obtained from the Hamiltonian, stochastic thermodynamics requires isothermal conditions and entropy proportional to position.