Resource Theory of Heat and Work with Non-commuting Charges
Khanian, Zahra Baghali (Universitat Autònoma de Barcelona. Departament de Física)
Bera, Manabendra Nath (Institut de Ciències Fotòniques)
Riera, Arnau (Institut de Ciències Fotòniques)
Lewenstein, Maciej (Institució Catalana de Recerca i Estudis Avançats)
Winter, Andreas (Universitat Autònoma de Barcelona. Departament de Física)

Date:	2023
Abstract:	We consider a theory of quantum thermodynamics with multiple conserved quantities (or charges). To this end, we generalize the seminal results of Sparaciari et al. (Phys. Rev. A 96:052112, 2017) to the case of multiple, in general non-commuting charges, for which we formulate a resource theory of thermodynamics of asymptotically many non-interacting systems. To every state we associate the vector of its expected charge values and its entropy, forming the phase diagram of the system. Our fundamental result is the Asymptotic Equivalence Theorem, which allows us to identify the equivalence classes of states under asymptotic approximately charge-conserving unitaries with the points of the phase diagram. Using the phase diagram of a system and its bath, we analyze the first and the second laws of thermodynamics. In particular, we show that to attain the second law, an asymptotically large bath is necessary. In the case that the bath is composed of several identical copies of the same elementary bath, we quantify exactly how large the bath has to be to permit a specified work transformation of a given system, in terms of the number of copies of the "elementary bath" systems per work system (bath rate). If the bath is relatively small, we show that the analysis requires an extended phase diagram exhibiting negative entropies. This corresponds to the purely quantum effect that at the end of the process, system and bath are entangled, thus permitting classically impossible transformations (unless the bath is enlarged). For a large bath, or many copies of the same elementary bath, system and bath may be left uncorrelated and we show that the optimal bath rate, as a function of how tightly the second law is attained, can be expressed in terms of the heat capacity of the bath. Our approach solves a problem from earlier investigations about how to store the different charges under optimal work extraction protocols in physically separate batteries.
Grants:	Ministerio de Economía y Competitividad FIS2016-86681-P Agencia Estatal de Investigación PID2019-107609GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1127 Ministerio de Economía y Competitividad CEX2019-000910-S Agencia Estatal de Investigación PID2019-106901GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1341 Agencia Estatal de Investigación PCI2019-111828-2 European Commission 899794
Note:	Altres ajuts: acords transformatius de la UAB
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Published in:	Annales Henri Poincare, Vol. 24, Issue 5 (May 2023) , p. 1725-1777, ISSN 1424-0661

DOI: 10.1007/s00023-022-01254-1

53 p, 1.1 MB

The record appears in these collections:
Articles > Research articles
Articles > Published articles