The Thermomajorization Polytope and Its Degeneracies

TL;DR

This paper explores the geometric structure of thermomajorization polytopes in quantum thermodynamics, introducing concepts of well-structured and stable Gibbs states and analyzing their implications for state transformations and degeneracies.

Contribution

It introduces the notions of well-structured and stable Gibbs states, and analyzes their impact on state transformations and degeneracies within the thermomajorization polytope.

Findings

Global cyclic state transfers are impossible if and only if the Gibbs state is stable.

Any subspace in equilibrium can be driven out of equilibrium via thermal operations.

Degenerate extreme points of the thermomajorization polytope witness subsystem equilibrium.

Abstract

Drawing inspiration from transportation theory, in this work we introduce the notions of "well-structured" and "stable" Gibbs states and we investigate their implications for quantum thermodynamics and its resource theory approach via thermal operations. It turns out that, in the quasi-classical realm, global cyclic state transfers are impossible if and only if the Gibbs state is stable. Moreover, using a geometric approach by studying the so-called thermomajorization polytope we prove that any subspace in equilibrium can be brought out of equilibrium via thermal operations. Interestingly, the case of some subsystem being in equilibrium can be witnessed via degenerate extreme points of the thermomajorization polytope, assuming the Gibbs state of the system is well structured. These physical considerations are complemented by simple new constructions for the polytope's extreme points as well as for an important class of extremal Gibbs-stochastic matrices.