Quantum Thermodynamic Integrability for Canonical and non-Canonical Statistics

Abstract

We extend the Carathéodory 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.

10 pages, 3 figures

References in corpus (17)

• Hawking Radiation as Tunneling
• Superstatistics
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Quantum Thermodynamic Cycles and quantum heat engines
• The Thermodynamics of Black Holes
• Canonical Typicality
• Black Hole Thermodynamics
• Quantum Heat Engine With Multi-Level Quantum Systems
• Hidden Messenger Revealed in Hawking Radiation: a Resolution to the Paradox of Black Hole Information Loss
• Estimate of temperature and its uncertainty in small systems
• Quantum Thermalization With Couplings
• Finite-bath corrections to the second law of thermodynamics
• Non-canonical statistics of finite quantum system
• Information-carrying Hawking radiation and the number of microstate for a black hole
• The uniqueness of the integration factor associated with the exchanged heat in thermodynamics
• Temperature fluctuations in mesoscopic systems