Strong Coupling Thermodynamics and Stochastic Thermodynamics from the Unifying Perspective of Time-Scale Separation

TL;DR

This paper develops a unified thermodynamic framework for small classical systems with strong environment interactions, leveraging time-scale separation to connect thermodynamics and stochastic thermodynamics.

Contribution

It introduces a theory based on the Hamiltonian of mean force that unifies thermodynamics and stochastic thermodynamics under strong coupling conditions.

Findings

Bath free energy is independent of system variables.

Weak coupling stochastic thermodynamics applies even with strong interactions.

Provides new insights into the origin of the second law.

Abstract

Assuming time-scale separation, a simple and unified theory of thermodynamics and stochastic thermodynamics is constructed for small classical systems strongly interacting with its environment in a controllable fashion. The total Hamiltonian is decomposed into a bath part and a system part, the latter being the Hamiltonian of mean force. Both the conditional equilibrium of bath and the reduced equilibrium of the system are described by canonical ensemble theories with respect to their own Hamiltonians. The bath free energy is independent of the system variables and the control parameter. Furthermore, the weak coupling theory of stochastic thermodynamics becomes applicable almost verbatim, even if the interaction and correlation between the system and its environment are strong and varied externally. Finally, this TSS-based approach also leads to some new insights about the origin of the second law of thermodynamics.