Work and entropy production in generalised Gibbs ensembles

Abstract

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.

Out-of-time-order correlations in the quasiperiodic Aubry-André model

“…In this appendix entry we review time evolution of free fermions and present out the numerical method required to carry out of quench protocol. For more detailed treatments of the time evolution of free fermions see [11], [77]. We are given in general a Hamiltonian written in the form,Ĥ…”

Thermodynamic resource theories, non-commutativity and maximum entropy principles

“…Our focus will be on notions of equilibrium based on the maximum entropy principle and complete passivity, and we will allow for the conserved quantities to be mutually non-commuting. For related works, see [11][12][13].…”

“…Extending equation (13) to other conserved quantities beyond energy, passivity and complete passivity can be defined in an analogous way:…”

Thermodynamic length in open quantum systems

“…The connection with the non-equilibrium free energy makes it extremely versatile and an extension to more general settings seems to be foreseeable with only minor modifications. For example, it should be possible to extend our approach to generalised Gibbs ensembles [59][60][61][62] simply by redefining the non equilibrium free energy (1) so to take into account the extra conserved quantities. We can even consider a dynamics which equilibrates to a non equilibrium steady states by simply substituting the thermal state in the definition (4) of the entropy production rate with the appropriate steady state π(H) [32].…”