Second law of thermodynamics for macroscopic mechanics coupled to thermodynamic degrees of freedom

TL;DR

This paper proves a maximum work principle for systems with macroscopic and microscopic degrees of freedom coupled via classical Hamiltonian dynamics, extending thermodynamic laws to such complex interactions.

Contribution

It establishes a maximum work principle based solely on Hamiltonian dynamics for coupled macroscopic and microscopic systems, without external driving.

Findings

Proves maximum work principle for coupled systems

Applies to impact, thermodynamic machines, molecular motors

Extends thermodynamic laws to microscopic-macroscopic interactions

Abstract

Based only on classical Hamiltonian dynamics, we prove the maximum work principle in a system where macroscopic dynamical degrees of freedom are intrinsically coupled to microscopic degrees of freedom. Unlike recent identities between irreversible work and free energy, such as in the Jarzynski relation, the macroscopic dynamics is not governed by an external action but undergoes the back reaction of the microscopic degrees of freedom. Our theorems cover such physical situations as impact between macroscopic bodies, thermodynamic machines, and molecular motors.