Second law of thermodynamics for batteries with vacuum state

Abstract

We study the implications of introducing vacuum state of the battery for arbitrary thermodynamic processes. Using the framework of thermal operations we derive a form of the second law which holds for batteries with bounded energy spectrum. In this form the second law gains corrections which vanish when battery is initialized far from the bottom of its spectrum. Furthermore, by studying a paradigmatic example of Landauer erasure we show that the existence of battery ground state leads to a thermodynamic behaviour which cannot be realized using an ideal weight. Surprisingly, this remains true even when battery operates far from its bottom. Our results are formulated in the language of quantum mechanics, but they can be similarily applied to classical (stochastic) systems as well.

An introductory review of the resource theory approach to thermodynamics

“…An incomplete list includes: the low temperature regime and the third law [76,103,104], interpolations between the single shot and average [64,105] as well as single-copy and collective [106] work extraction regimes, fluctuation theorems in the resource theory context [40,[107][108][109], relating the resource theory framework to the axiomatic approach of Lieb and Yngvason [12,110], correlations in the single-shot regime [111][112][113] (including quantum coherence [96,114]) limits to catalysis [115], explorations beyond i.i.d. limits [77,116], i.i.d in many-body systems [117], approximate transformations [118][119][120], finite heat capacities [66], conditioned thermal operations [121], Gaussian thermal operations [122,123], study of the role of batteries [124], thermodynamics of quantum channels [125], optimal cooling protocols [16] and many more directions more or less tightly related to the framework described here (see, e.g. references in [2][3][4]126]).…”

Thermodynamics of Minimal Coupling Quantum Heat Engines

“…In this paper we attempt to substantially advance the above basic problem by considering the following class of engines, which we call minimal-coupling engines: (i) the time evolution consists of discrete steps, each being an energy preserving unitary acting on two systems only, (ii) an explicit, translationally invariant battery is included -the so-called ideal weight [14,41,42] (see also [43] for the discussion of the physicality of the model). Our engines thus consist of four systems: the hot and cold bath, the working body and the battery.…”