Quantum Euler relation for local measurements

TL;DR

This paper derives a quantum analog of the classical Euler relation, linking internal energy to local measurements, and demonstrates its validity in a collective dissipation model showing thermodynamic behavior at weak coupling.

Contribution

It introduces a quantum Euler relation based on local measurement information, extending classical thermodynamics to quantum systems with measurement back action.

Findings

Quantum Euler relation is valid for collective dissipation models.

Thermodynamic behavior emerges in the weak-coupling regime.

Measurement back action influences quantum thermodynamic relations.

Abstract

In classical thermodynamics the Euler relation is an expression for the internal energy as a sum of the products of canonical pairs of extensive and intensive variables. For quantum systems the situation is more intricate, since one has to account for the effects of the measurement back action. To this end, we derive a quantum analog of the Euler relation, which is governed by the information retrieved by local quantum measurements. The validity of the relation is demonstrated for the collective dissipation model, where we find that thermodynamic behavior is exhibited in the weak-coupling regime.