Local temperature of out-of-equilibrium quantum electron systems

Abstract

We show how the local temperature of out-of-equilibrium, quantum electron systems can be consistently defined with the help of an external voltage and temperature probe. We determine sufficient conditions under which the temperature measured by the probe (i) is independent of details of the system-probe coupling, (ii) is equal to the temperature obtained from an independent current-noise measurement, (iii) satisfies the transitivity condition expressed by the zeroth law of thermodynamics, and (iv) is consistent with Carnot's theorem. This local temperature therefore characterizes the system in the common sense of equilibrium thermodynamics, but remains well defined even in out-of-equilibrium situations with no local equilibrium.

Cold spots in quantum systems far from equilibrium: Local entropies and temperatures near absolute zero

“…The s p distribution strongly resembles the temperature distribution shown in Fig. 2, consistent with the fact (14) that the equilibrium entropy of a system of fermions is proportional to temperature at low temperatures. This resemblence is only manifest in the properlynormalized entropy per state s p ; the spatial variations of S p are much larger, and stem from the orders-of- The deviation from local equilibrium is quantified by the local entropy deficit ∆s = s p − s s shown in the top right panel of Fig.…”

“…The above definition of T p is operational: temperature is that which is measured by a suitably defined thermometer. Nonetheless, it has been shown that this definition of T p is consistent with the laws of thermodynamics under certain specified conditions 14,16 . In the present article, we show that T p is consistent with the third law of thermodynamics.…”

Thermodynamic meaning of local temperature of nonequilibrium open quantum systems

“…The definition of local temperature based on the ZCC has been used extensively in the literature [29,32,34,35,[40][41][42][43][44]. The basic idea is to couple an ideal potentiometer/thermometer (the probe) to the nonequilibrium system of interest.…”

“…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.…”

“…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.…”