Entropy production and heat transport in harmonic chains under time-dependent periodic drivings

Abstract

Using stochastic thermodynamics, the properties of interacting linear chains subject to periodic drivings are investigated. The systems are described by Fokker-Planck-Kramers equation and exact (explicit) solutions are obtained for periodic drivings as functions of the modulation frequency and strength constants. The limit of long chains is analyzed by means of a protocol in which the intermediate temperatures are self-consistently chosen and the entropy production is decomposed as a sum of two individual contributions, one coming from real baths (placed at extremities of lattice) and other from self-consistent baths. The thermal reservoirs lead to a heat flux according to Fourier's law. Explicit expressions for short chains are derived, whose entropy production is written down as a bilinear function of thermodynamic forces and the associated fluxes, from which Onsager coefficients have been evaluated. A comparison between distinct periodic drivings is also performed.

Diffusive Hydrodynamics of Inhomogenous Hamiltonians

“…showing (1.27). It should be stressed that equation (1.25) generalises the entropy production rate induced by thermodynamic forces found by Onsager [31,32] (see also more recent works [56][57][58]) to a system with n conserved quantities and external inhomogeneous force fields. Analogously to the work of Kubo [59] we here prove positivity of entropy increase by the definition of the extended Onsager coefficients.…”

Maximal power for heat engines: role of asymmetric interaction times

“…Such a remarkable finding has also been derived in several distinct works (see e.g. [7,8]) and despite not possessing the same universal status of the Carnot efficiency, it provides a powerful guide about the operation of nonequilibrum engines under more realistic situations and sheds light on the construction and performance of small-scale engines (nanoscopic devices) working at maximum power regime from the tools of stochastic thermodynamics [2,3,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. In this context, single-level quantum dots have been proposed as proto-type machines, whose simplicity allows detailed investigation of their performances at maximum power [23][24][25].…”

Obtaining efficient thermal engines from interacting Brownian particles under time dependent periodic drivings

“…Our aim is to study the effect that interactions have on the performance of an engine. To do this, we will focus on the simplest case in which particles are subject to harmonic time-dependent forces F i (t) of different amplitude, same frequency ω, but with a lag δ between them [18,38,43,46]…”

“…Most of them are based on single particle engines and have been studied for theoretical [25][26][27][28][29][30][31][32][33][34] and experimental [15,35,36] settings. On the other hand, the number of studies on the thermodynamic properties of interacting chains of particles are limited and often constrained to timeindependent driving [24,37,38]. The scarcity of results, together the richness of such system, raises distinct and relevant questions about the interaction contribution to the performance, the interplay between interaction and driving forces and choice of protocol optimization.…”