Minimal Work Principle and its Limits for Classical Systems

TL;DR

This paper examines the validity and limitations of the minimal work principle in classical systems, showing it holds for ergodic systems but may fail for non-ergodic ones, with examples and experimental considerations.

Contribution

It clarifies the conditions under which the minimal work principle applies in classical Hamiltonian systems, highlighting its limitations for non-ergodic systems.

Findings

The principle holds for ergodic systems.

It may fail for non-ergodic systems depending on conditions.

Examples demonstrate the principle's limits and experimental implications.

Abstract

The minimal work principle asserts that work done on a thermally isolated equilibrium system, is minimal for the slowest (adiabatic) realization of a given process. This principle, one of the formulations of the second law, is operationally well-defined for any finite (few particle) Hamiltonian system. Within classical Hamiltonian mechanics, we show that the principle is valid for a system of which the observable of work is an ergodic function. For non-ergodic systems the principle may or may not hold, depending on additional conditions. Examples displaying the limits of the principle are presented and their direct experimental realizations are discussed.