Generalization of the detailed fluctuation theorem for Non-Hamiltonian Dynamics

TL;DR

This paper extends the detailed fluctuation theorem to non-Hamiltonian systems, demonstrating its broad applicability and connection to thermodynamic principles without relying on traditional assumptions.

Contribution

It derives a generalized fluctuation theorem for non-Hamiltonian dynamics, unifying various thermostatting schemes within a non-Hamiltonian phase space framework.

Findings

The theorem applies to multiple thermostatting schemes.

Recovers detailed balance in equilibrium.

Reproduces Jarzynski's work theorem for driven systems.

Abstract

Detailed fluctuation theorem, a microscopic version of the steady state fluctuation theorem, has been proposed by Jarzynski and demonstrated in the case of Hamiltonian systems weakly coupled with reservoirs. We show that an identical theorem for phase space compressibility rate can be derived for systems evolving under non-Hamiltonian extended system dynamics, without certain limiting assumptions made in the original work. Our derivation is based on the non-Hamiltonian phase space formulation of statistical mechanics and does not rely on any assumptions of thermodynamic nature. This version of the detailed fluctuation theorem is shown to be generic enough to be applicable to several thermostatting schemes. It is shown that in equilibrium, this detailed fluctuation theorem boils down to the detailed balance equation and it is further shown to reproduce the Jarzynski's work theorem for driven systems.