Adiabatic processes need not correspond to optimal work

TL;DR

This paper investigates the validity of the minimum work principle in finite quantum systems, showing it holds without level crossing but can be violated when levels cross, indicating optimal work processes may not be adiabatically slow or reversible.

Contribution

It demonstrates the conditions under which the minimum work principle applies or fails in quantum systems, highlighting the role of energy level crossings.

Findings

Minimum work principle holds if energy levels do not cross.

Level crossing can violate the minimum work principle.

Optimal work processes may be non-adiabatic and irreversible.

Abstract

The minimum work principle states that work done on a thermally isolated equilibrium system is minimal for the adiabatically slow (reversible) realization of a given process. This principle, one of the formulations of the second law, is studied here for finite (possibly large) quantum systems interacting with macroscopic sources of work. It is shown to be valid as long as the adiabatic energy levels do not cross. If level crossing does occur, counter examples are discussed, showing that the minimum work principle can be violated and that optimal processes are neither adiabatically slow nor reversible.