Dissipative work, Clausius inequality, and microscopic reversibility for open Hamiltonian systems

TL;DR

This paper derives a microscopic form of the Clausius inequality for open Hamiltonian systems and demonstrates the positivity of dissipative work, linking thermodynamic irreversibility with microscopic reversibility.

Contribution

It introduces a microscopic expression of the Clausius inequality and establishes the positivity of dissipative work within Hamiltonian dynamics for open systems.

Findings

Microscopic expression of the Clausius inequality derived

Positivity of dissipative work demonstrated

Connection between microscopic reversibility and thermodynamic irreversibility established

Abstract

We derive a microscopic expression of the Clausius inequality for isothermal open systems within the fundamental Hamiltonian dynamics. We also show the positivity of the dissipative work, which is a path integral generalization of the so-called relative entropy for the probability functionals of time forward- and reversed- trajectories.