O the Foundations of Quantum Thermodynamics.

David Z. Albert

A. D. Jannussis

Ronnie Kosloff

Quantum thermodynamics addresses the emergence of thermodynamic laws from quantum mechanics. The viewpoint advocated is based on the intimate connection of quantum thermodynamics with the theory of open quantum systems. Quantum mechanics inserts dynamics into thermodynamics, giving a sound foundation to finite-time-thermodynamics. The emergence of the 0-law, I-law, II-law and III-law of thermodynamics from quantum considerations is presented. The emphasis is on consistency between the two theories, which address the same subject from different foundations. We claim that inconsistency is the result of faulty analysis, pointing to flaws in approximations.

Felix C. Binder, Luis Alfonso Correa, Christian Gogolin +2 more

Akira Suzuki, Hisao Taira

It is proposed a representation of the basic laws (i.e. the zeroth, first, second and third laws) in thermodynamics for quantum systems in the pure and mixed ensembles, respectively. We show that the basic laws are represented by parameters that specify respective quantum states. The parameters are the elements of the thermodynamic state space Mθ and the state space Mϑ of the mixed ensemble for quantum systems. The introduction of such parameters is based on a probabilistic nature of quantum theory. Consistency between quantum theory and classical thermodynamics is preserved throughout the formulation for the representation of the thermodynamical laws in quantum systems (quantum thermodynamics). The present theory gives the mathematical foundations of quantum thermodynamics.

Ruo-Xun Zhai, Che Sun

We extend the Carathéodory principle of the second law to quantum thermodynamics, where energy levels depend on macroscopic variables such as volume and magnetic field. This extension introduces the concept of quantum thermodynamic integrability (QTI), providing an alternative foundation for statistical mechanics. QTI is characterized by the path independence of work and heat within the thermodynamic manifold, locally described by energy levels and specific thermodynamic parameters. Within this framework, temperature naturally emerges as an integrating factor, enabling the derivation of both canonical and noncanonical states from the entropy integrable equations based on QTI. Notably, noncanonical states, which become particularly significant outside the thermodynamic limit, reveal the existence of informational correlations in finite-size thermodynamic systems.