Statistical work-energy theorems in deterministic dynamics

TL;DR

This paper provides a theoretical analysis of work-energy theorems in deterministic systems coupled to heat reservoirs, deriving conditions for nonequilibrium equalities and exploring their dependence on time-reversal symmetry.

Contribution

It formulates a general statistical framework for work-energy relations in nonequilibrium deterministic systems and examines the role of time-reversal invariance.

Findings

Derived a consistency condition for nonequilibrium work theorems.

Demonstrated the utility of the framework through examples.

Showed that symmetry of fluctuations depends on time-reversal invariance.

Abstract

We theoretically explore the Bochkov-Kuzovlev-Jarzynski-Crooks work theorems in a finite system subject to external control, which is coupled to a heat reservoir. We first elaborate the mechanical energy-balance between the system and the surrounding reservoir and proceed to formulate the statistical counterpart under the general nonequilibrium conditions. Consequently, a consistency condition is derived, underpinning the nonequilibrium equalities, both in the framework of the system-centric and nonautonomous Hamiltonian pictures and its utility is examined in a few examples. Also, we elucidate that the symmetric fluctuation associated with forward and backward manipulation of the nonequilibrium work is contingent on time-reversal invariance of the underlying mesoscopic dynamics.