Thermodynamic meaning of local temperature of nonequilibrium open quantum systems

Abstract

Measuring the local temperature of nanoscale systems out of equilibrium has emerged as a new tool to study local heating effects and other local thermal properties of systems driven by external fields. Although various experimental protocols and theoretical definitions have been proposed to determine the local temperature, the thermodynamic meaning of the measured or defined quantities remains unclear. By performing analytical and numerical analysis of bias-driven quantum dot systems both in the noninteracting and strongly-correlated regimes, we elucidate the underlying physical meaning of local temperature as determined by two definitions: the zero-current condition that is widely used but not measurable, and the minimal-perturbation condition that is experimentally realizable. We show that, unlike the zero-current one, the local temperature determined by the minimalperturbation protocol establishes a quantitative correspondence between the nonequilibrium system of interest and a reference equilibrium system, provided the probed system observable and the related electronic excitations are fully local. The quantitative correspondence thus allows the wellestablished thermodynamic concept to be extended to nonequilibrium situations.PACS numbers: 05.70. Ln, 71.27.+a, 73.23.Hk, 73.63.Kv Probing the variation of local temperatures in systems out of equilibrium has become a subject of intense experimental interest in physics [1][2][3][4][5], chemistry [6][7][8] and life sciences [9][10][11][12]. With the development of high-resolution thermometry techniques, measurement of some sort of temperature distributions of nonequilibrium systems has been realized, such as in graphene-metal contacts [4], gold interconnect structures [5], and living cells [12].Local electronic and phononic excitations occur in nanoelectronic devices subject to a bias voltage or thermal gradient, and hence the devices are supposedly at a local temperature somewhat higher than the background temperature. Such local heating affects crucially the device properties [13][14][15][16], and have significant influence on some physical processes, such as thermoelectric conversion [17][18][19], heat dissipation [8,19], and electron-phonon interactions [20,21]. All these studies, however, leave open the question of what precisely is a "local temperature" in a nonequilibrium system, a concept that has a well-established meaning only in global equilibrium.Over the past decade, numerous experimental [15,[22][23][24][25][26][27] and theoretical [28][29][30][31][32][33][34][35][36][37][38] efforts have been made to provide practical and meaningful definitions of local temperature for nonequilibrium systems that bear a close conceptual resemblance to the thermodynamic one. However, it has remained largely unclear how to physically interpret the defined local temperature, and how to associate the measured value with the magnitudes of local excitations and local heating at a quantitative level.This work aims at elucidating these fundamental issues through analyti...

Local temperatures out of equilibrium

“…Such a minimal perturbation condition (MPC) can be examined by monitoring the evolution of a certain thermosensitive property of the system [140]. As a consequence, operational protocols based on the MPC have been proposed, with which the local temperature can be determined quantitatively by presuming the local equilibrium approximation [182,183].…”

“…1.3) may become independent of each other. For instance, it is difficult to define a unique local temperature if nonlocal excitations emerge in the system [183]. Second, the practical implementation of a theoretical definition may involve non-universal approximation or parametrization procedure.…”

“…The temperature gradient across two leads is set to zero, T R = T L = T . Reprinted with permission from[183]. Copyright 2016 American Physical Society.…”

Performance of theT-matrix based master equation for Coulomb drag in double quantum dots

“…The numerical implementation of the HEOM formalism, usually termed HEOM, can capture the combined effects of system-reservoir dissipation, many-body interactions, and non-Markovian memory in a nonperturbative manner. The HEOM approach is applicable to both static and dynamic properties of diverse quantum impurity systems [55][56][57][58][59][60][61][62][63][64][65]. Moreover, it has also been combined with the density-functional theory to study the correlated electronic structure of adsorbed magnetic molecules [66][67][68].…”

Charge Transport and Entropy Production Rate in Magnetically Active Molecular Dimer

“…From the same standpoint, thermal transport studies were conceived and came to be conclusive in the upcoming years [2]. Subsequently, several theoretical studies demonstrated the possibility to conduct both thermal and charge through tunneling junctions [26][27][28][29][30][31][32][33][34], both in presence and absence of lattice vibrations, although there is no generic framework that successfully is capable of describing the thermodynamic properties of nano junctions [8,14,35].…”