Consistent thermodynamics for spin echoes

TL;DR

This paper presents a thermodynamic framework for spin echoes that accounts for correlations between spin and translational degrees of freedom, showing that entropy does not decrease during echoes and aligning with the second law.

Contribution

It introduces an entropy functional based on Boltzmann macrostates that includes both spin and translational degrees of freedom, clarifying the thermodynamics of spin echoes.

Findings

Spin echoes do not involve entropy decrease when correlations are considered.

Dephasing corresponds to Hamiltonian evolution, not entropy change.

Decay of net magnetization accurately measures entropy change.

Abstract

Spin-echo experiments are often said to constitute an instant of anti-thermodynamic behavior in a concrete physical system that violates the second law of thermodynamics. We argue that a proper thermodynamic treatment of the effect should take into account the correlations between the spin and translational degrees of freedom of the molecules. To this end, we construct an entropy functional using Boltzmann macrostates that incorporates both spin and translational degrees of freedom. With this definition there is nothing special in the thermodynamics of spin echoes: dephasing corresponds to Hamiltonian evolution and leaves the entropy unchanged; dissipation increases the entropy. In particular, there is no phase of entropy decrease in the echo. We also discuss the definition of macrostates from the underlying quantum theory and we show that the decay of net magnetization provides a faithful measure of entropy change.