Unification of the first law of quantum thermodynamics

TL;DR

This paper unifies various quantum thermodynamic formulations of the first law by leveraging quantum mechanics and dynamical symmetries, clarifying how energy changes are partitioned into work and heat.

Contribution

It provides a comprehensive framework that bridges five different approaches to the quantum first law, resolving ambiguities in energy partitioning.

Findings

Unified framework for quantum first law

Reconciliation of autonomous and semi-classical approaches

Clarification of work and heat definitions in quantum systems

Abstract

Underlying the classical thermodynamic principles are analogous microscopic laws, arising from the fundamental axioms of quantum mechanics. These define quantum thermodynamic variables such as quantum work and heat and characterize the possible transformations of open quantum systems. The foremost quantum thermodynamic law is a simple statement concerning the conservation of energy. Nevertheless, there exist ambiguity and disagreement regarding the precise partition of a quantum system's energy change to work and heat. By treating quantum mechanics as a comprehensive theory, applicable to both the micro and macroscopic domains, and employing dynamical symmetries, we bridge the gaps between five popular thermodynamic approaches to the first law. These include both autonomous and semi-classical formulations, which define work in terms of an ensemble average, as well as the single shot paradigm, where work is defined as a deterministic quantity.