TY - JOUR

T1 - Work and entropy production in generalised Gibbs ensembles

AU - Perarnau-Llobet, Marti

AU - Riera, Arnau

AU - Gallego, Rodrigo

AU - Wilming, Henrik

AU - Eisert, Jens

PY - 2016/12/23

Y1 - 2016/12/23

N2 - Recent years have seen an enormously revived interest in the study of thermodynamic notions in the quantum regime. This applies both to the study of notions of work extraction in thermal machines in the quantum regime, as well as to questions of equilibration and thermalisation of interacting quantum many-body systems as such. In this work we bring together these two lines of research by studying work extraction in a closed system that undergoes a sequence of quenches and equilibration steps concomitant with free evolutions. In this way, we incorporate an important insight from the study of the dynamics of quantum many body systems: the evolution of closed systems is expected to be well described, for relevant observables and most times, by a suitable equilibrium state. We will consider three kinds of equilibration, namely to (i) the time averaged state, (ii) the Gibbs ensemble and (iii) the generalised Gibbs ensemble, reflecting further constants of motion in integrable models. For each effective description, we investigate notions of entropy production, the validity of the minimal work principle and properties of optimal work extraction protocols. While we keep the discussion general, much room is dedicated to the discussion of paradigmatic non-interacting fermionic quantum many-body systems, for which we identify significant differences with respect to the role of the minimal work principle. Our work not only has implications for experiments with cold atoms, but also can be viewed as suggesting a mindset for quantum thermodynamics where the role of the external heat baths is instead played by the system itself, with its internal degrees of freedom bringing coarse-grained observables to equilibrium.

AB - Recent years have seen an enormously revived interest in the study of thermodynamic notions in the quantum regime. This applies both to the study of notions of work extraction in thermal machines in the quantum regime, as well as to questions of equilibration and thermalisation of interacting quantum many-body systems as such. In this work we bring together these two lines of research by studying work extraction in a closed system that undergoes a sequence of quenches and equilibration steps concomitant with free evolutions. In this way, we incorporate an important insight from the study of the dynamics of quantum many body systems: the evolution of closed systems is expected to be well described, for relevant observables and most times, by a suitable equilibrium state. We will consider three kinds of equilibration, namely to (i) the time averaged state, (ii) the Gibbs ensemble and (iii) the generalised Gibbs ensemble, reflecting further constants of motion in integrable models. For each effective description, we investigate notions of entropy production, the validity of the minimal work principle and properties of optimal work extraction protocols. While we keep the discussion general, much room is dedicated to the discussion of paradigmatic non-interacting fermionic quantum many-body systems, for which we identify significant differences with respect to the role of the minimal work principle. Our work not only has implications for experiments with cold atoms, but also can be viewed as suggesting a mindset for quantum thermodynamics where the role of the external heat baths is instead played by the system itself, with its internal degrees of freedom bringing coarse-grained observables to equilibrium.

KW - entropy production

KW - equilibration

KW - generalised Gibbs ensembles

KW - quantum thermodynamics

KW - thermalisation

KW - work extraction

UR - http://www.scopus.com/inward/record.url?scp=85007583916&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/aa4fa6

DO - 10.1088/1367-2630/aa4fa6

M3 - Article

AN - SCOPUS:85007583916

VL - 18

JO - New journal of physics

JF - New journal of physics

SN - 1367-2630

IS - 12

M1 - 123035

ER -