The temperature of a physical system is operationally defined in physics as "that quantity which is measured by a thermometer" weakly coupled to, and at equilibrium with the system. This definition is unique only at global equilibrium in view of the zeroth law of thermodynamics: when the system and the thermometer have reached equilibrium, the "thermometer degrees of freedom" can be traced out and the temperature read by the thermometer can be uniquely assigned to the system. Unfortunately, such a procedure cannot be straightforwardly extended to a system out of equilibrium, where local excitations may be spatially inhomogeneous and the zeroth law of thermodynamics does not hold. With the advent of several experimental techniques that attempt to extract a single parameter characterizing the degree of local excitations of a (mesoscopic or nanoscale) system out of equilibrium, this issue is making a strong comeback to the forefront of research. In this paper, we will review the difficulties to define a unique temperature out of equilibrium, the majority of definitions that have been proposed so far, and discuss both their advantages and limitations. We will then examine a variety of experimental techniques developed for measuring the non-equilibrium local temperatures under various conditions. Finally we will discuss the physical implications of the notion of local temperature, and present the practical applications of such a concept in a variety of nanosystems out of equilibrium.

中文翻译：

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局部温度失衡

物理系统的温度在物理学中在操作上定义为“由温度计测量的量”，与系统弱耦合并处于平衡状态。考虑到热力学第零定律，这个定义只有在全局平衡时才唯一：当系统和温度计达到平衡时，“温度计自由度”可以被追踪，温度计读取的温度可以唯一分配给系统。不幸的是，这样的过程不能直接扩展到平衡之外的系统，其中局部激发可能在空间上是不均匀的，并且热力学第零定律不成立。随着几种实验技术的出现，这些技术试图提取表征（介观或纳米级）系统脱离平衡的局部激发程度的单个参数，这个问题正在强势回归研究的前沿。在本文中，我们将回顾定义一个独特的非平衡温度的困难，以及迄今为止提出的大多数定义，并讨论它们的优点和局限性。然后，我们将研究为测量各种条件下的非平衡局部温度而开发的各种实验技术。最后，我们将讨论局部温度概念的物理含义，并介绍这种概念在各种非平衡纳米系统中的实际应用。