Quantum Thermodynamic Integrability for Canonical and non-Canonical Statistics

TL;DR

This paper introduces Quantum Thermodynamic Integrability (QTI), extending the Second Law to quantum systems with variable energy levels, providing a new foundation for understanding canonical and non-canonical states, especially in finite systems.

Contribution

It develops the concept of QTI as a path-independent framework for quantum thermodynamics, linking energy levels, thermodynamic parameters, and entropy to derive states beyond the thermodynamic limit.

Findings

QTI characterizes path-independence of work and heat in quantum systems.

Temperature emerges naturally as an integrating factor in QTI.

Non-canonical states exhibit informational correlations in finite-size systems.

Abstract

We extend the Carath\'{e}odory principle of the Second Law to quantum thermodynamics with energy levels depending on macroscopic variables, such as volume and magnetic field. This extension introduces the concept of Quantum Thermodynamic Integrability (QTI), offering an alternative foundation for statistical mechanics. QTI is characterized by the path-independence of work and heat within the thermodynamic manifold, which is locally described by energy levels and specific thermodynamic parameters. Within this framework, temperature naturally emerges as an integrating factor, allowing for the derivation of both canonical and non-canonical states from the Entropy Integrable Equations (EIE) based on QTI. Notably, non-canonical states, which become particularly significant outside the thermodynamic limit, reveal the existence of informational correlations in finite-size thermodynamic systems.