标题： 托尔曼效应的代价：关于广义相对论中经典温度的状态 显示英文标题

标题： The Toll of the Tolman Effect: On the Status of Classical Temperature in General Relativity

摘要： 在相对论宇宙学中，托尔曼效应是众所周知的，但在该领域之外很少被讨论。这令人惊讶，因为该效应——在引力势变化的系统中，即使处于热平衡也会表现出温度梯度——与普通的经典热力学相冲突。在本文中，我们试图从基础的角度更好地理解这一效应。我们提出了五个观点。首先，正如托尔曼所知，是爱因斯坦首次发现了这一效应，而且爱因斯坦的推导有助于我们认识到该效应的稳固性。其次，以“局部温度”来解释该效应会导致经典热力学的大部分内容崩溃。第三，通过使用爱因斯坦偏好的“真正温度”——我们将称之为全局温度——可以挽救热力学，但这也有一些代价。第四，该效应最好通过钟表而不是能量损失来理解。第五，受爱因斯坦其他地方的一个提议启发，我们勾勒出一种基于第三种新温度的解释，我们称之为“真正局部温度”。在这种观点下，温度——以及热力学——仅相对于局部钟表来定义。总之，我们认为热力学中温度的碎片化是广义相对论中时间碎片化的自然且可预期的结果。 显示英文摘要

摘要： The Tolman effect is well-known in relativistic cosmology but rarely discussed outside it. That is surprising because the effect -- that systems extended over a varying gravitational potential exhibit temperature gradients while in thermal equilibrium -- conflicts with ordinary classical thermodynamics. In this paper we try to better understand this effect from a foundational perspective. We make five claims. First, as Tolman knew, it was Einstein who first discovered the effect, and furthermore, Einstein's derivation helps us appreciate how robust it is. Second, the standard interpretation of the effect in terms of 'local temperature' leads to the breakdown of much of classical thermodynamics. Third, one can rescue thermodynamics by using Einstein's preferred interpretation in terms of the 'wahre Temperatur' -- what we'll call global temperature -- but it too has some costs. Fourth, the effect is perhaps best understood in terms of clocks as opposed to energy loss. Fifth, inspired by a proposal of Einstein's elsewhere, we sketch an interpretation of the effect in terms of a third novel temperature, which we call the 'wahre-local temperature'. On this view, temperature -- and thermodynamics -- is defined only in relation to local clocks. In sum, we view the fragmentation of temperature in thermodynamics as a natural and expected result of the fragmentation of time in general relativity.