Gauge invariant quantum thermodynamics: consequences for the first law

Abstract: Universality of classical thermodynamics rests on the central limit theorem, due to which, measurements of thermal fluctuations are unable to reveal detailed information regarding the microscopic structure of a macroscopic body. When small systems are considered and fluctuations become important, thermodynamic quantities can be understood in the context of classical stochastic mechanics. A fundamental assumption behind thermodynamics is therefore that of coarse-graning, which stems from a substantial lack of control over all degrees of freedom. However, when quantum systems are concerned, one claims a high level of control. As a consequence, information theory plays a major role in the identification of thermodynamic functions. Here, drawing from the concept of gauge symmetry, essential in all modern physical theories, we put forward a new possible, intermediate route. Working within the realm of quantum thermodynamics we explicitly construct physically motivated gauge transformations which encode a gentle variant of coarse-graining behind thermodynamics. As a consequence, we reinterpret quantum work and heat, as well as the role of quantum coherence.