Quantum thermodynamics as a gauge theory

TL;DR

This paper develops a gauge-invariant framework for quantum thermodynamics, incorporating energy degeneracies and defining entropy, thereby unifying thermodynamic and quantum principles with applications to critical systems.

Contribution

It extends previous gauge theory of quantum thermodynamics by including energy degeneracies and introducing a gauge-invariant entropy measure.

Findings

Incorporates energy spectrum degeneracies into the gauge theory.

Defines a gauge-invariant entropy and explores its properties.

Applies the framework to critical quantum systems.

Abstract

Thermodynamics is based on a coarse-grained approach, from which its fundamental variables emerge, effectively erasing the complicate details of the microscopic dynamics within a macroscopic system. The strength of Thermodynamics lies in the universality provided by this paradigm. In contrast, quantum mechanics focuses on describing the dynamics of microscopic systems, aiming to make predictions about experiments we perform, a goal shared by all fundamental physical theories, which are often framed as gauge theories in modern physics. Recently, a gauge theory for quantum thermodynamics was introduced, defining gauge invariant work and heat, and exploring their connections to quantum phenomena. In this work, we extend that theory in two significant ways. First, we incorporate energy spectrum degeneracies, which were previously overlooked. Additionally, we define gauge-invariant entropy, exploring its properties and connections to other physical and informational quantities. This results in a complete framework for quantum thermodynamics grounded in the principle of gauge invariance. To demonstrate some implications of this theory, we apply it to well-known critical systems.