Related papers: Dissipation, interaction and relative entropy
Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological, and social processes. The…
We discuss that the thermodynamics of composite systems with non-additive entropies and additive energies can be equivalently derived considering additive entropies and non-additive energies. The general discussion is illustrated by a…
In classical thermodynamics the Euler relation is an expression for the internal energy as a sum of the products of canonical pairs of extensive and intensive variables. For quantum systems the situation is more intricate, since one has to…
In quantum systems, entropy production is typically defined as the quantum relative entropy between two states. This definition provides an upper bound for any flux (of particles, energy, entropy, etc.) of bounded observables, which proves…
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and second law are formulated consistently. In the linear response regime,…
Given a thermodynamic process which carries a system from one equilibrium state to another, we construct a quantity whose average, over an ensemble of microscopic realizations of the process, depends only on these end states, even if at…
The thermodynamic and kinetic uncertainty relations indicate trade-offs between the relative fluctuation of observables and thermodynamic quantities such as dissipation and dynamical activity. Although these relations have been well studied…
A time-dependent product is introduced between the observables of a dissipative quantum system, that accounts for the effects of dissipation on observables and commutators. In the $t \to \infty$ limit this yields a contracted algebra. The…
It is shown that the von Neumann entropy, a measure of quantum entanglement, does have its classical counterpart in thermodynamic systems, which we call partial entropy. Close to the critical temperature the partial entropy shows perfect…
We give a proof of transient fluctuation relations for the entropy production (dissipation function) in nonequilibrium systems, which is valid for most time reversible dynamics. We then consider the conditions under which a transient…
Two identical finite quantum systems prepared initially at different temperatures, isolated from the environment, and subsequently brought into contact are demonstrated to relax towards Gibbs-like quasi-equilibrium states with a common…
The entropy of an ergodic source is the limit of properly rescaled 1-block entropies of sources obtained applying successive non-sequential recursive pairs substitutions (see P. Grassberger 2002 ArXiv:physics/0207023 and D. Benedetto, E.…
We extend entropy production to a deeply quantum regime involving noncommuting conserved quantities. Consider a unitary transporting conserved quantities ("charges") between two systems initialized in thermal states. Three common formulae…
The asymptotic correspondence between the probability mass function of the $q$-deformed multinomial distribution and the $q$-generalised Kullback-Leibler divergence, also known as Tsallis relative entropy, is established. The probability…
We study nonequilibrium thermodynamic properties of a driven one-dimensional quantum fluid by combining nonlinear Luttinger liquid theory with the quantum kinetic equation. In particular, we derive an entropy production consistent with the…
The fluctuation-dissipation relation is usually formulated for a system interacting with a heat bath at finite temperature in the context of linear response theory, where only small deviations from the mean are considered. We show that for…
This work presents a general unifying theoretical framework for quantum non-equilibrium systems. It is based on a re-statement of the dynamical problem as one of inferring the distribution of collision events that move a system toward…
We establish that entropy production, which is crucial to the characterization of thermodynamic irreversibility, is obtained through a variational principle involving the Kulback-Leibler divergence. A simple application of this…
It is argued that a typical many body energy eigenstate has a well defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems…
Von Neumann entropy rate for open quantum systems is, in general, written in terms of entropy production and entropy flow rates, encompassing the second law of thermodynamics. When the open-quantum-system evolution corresponds to a quantum…