Violation of all the second laws of thermal operations by inhomogeneous reservoirs

TL;DR

This paper demonstrates that inhomogeneous reservoirs can violate the expected monotonic decrease of generalized free energies in thermodynamic processes, challenging the robustness of the second laws in resource theory.

Contribution

It shows that small inhomogeneities in reservoirs can lead to violations of all second laws of thermal operations, revealing limitations of current thermodynamic frameworks.

Findings

Generalized free energies can increase under inhomogeneous conditions.

Violations occur even with small perturbations from ideal reservoirs.

Geometric representation explains the observed violations.

Abstract

In the resource theory of thermodynamics, the decrease of the free energy based on von Neumann entropy is not a sufficient condition to determine free evolution. Rather, a whole family of generalised free energies $F_{\alpha}$ must be monotonically decreasing. We study the resilience of this result to relaxations of the framework. We use a toy collisional model, in which the deviations from the ideal situation can be described as arising from inhomogeneities of local fields or temperatures. For any small amount of perturbation, we find that there exist initial states such that both single-shot and averaged values of $F_{\alpha}$ do not decrease monotonically for all $\alpha>0$. A geometric representation accounts for the observed behavior in a graphic way.