Hamiltonian derivation of a detailed fluctuation theorem

TL;DR

This paper derives a detailed fluctuation theorem for far-from-equilibrium systems using Hamiltonian mechanics, explicitly including heat reservoirs, and relates it to steady-state fluctuation theorems and free energy relations.

Contribution

It introduces a Hamiltonian-based derivation of a detailed fluctuation theorem that accounts for heat reservoirs explicitly, extending the theoretical framework of nonequilibrium thermodynamics.

Findings

Derived a hybrid fluctuation theorem incorporating heat reservoirs

Connected the result to steady-state fluctuation theorem

Established a far-from-equilibrium free energy relation

Abstract

We analyze the microscopic evolution of a system undergoing a far-from-equilibrium thermodynamic process. Explicitly accounting for the degrees of freedom of participating heat reservoirs, we derive a hybrid result, similar in form to both the fluctuation theorem, and a statement of detailed balance. We relate this result to the steady-state fluctuation theorem, and to a free energy relation valid far from equilibrium.