Building on the idea of Tolman and Ehrenfest that heat has weight, Luttinger established a deep connection between gravitational fields and thermal transport. However, this relation does not include anomalous quantum fluctuations that become paramount in strongly curved spacetime. In this work, we revisit the celebrated Tolman-Ehrenfest and Luttinger relations and show how to incorporate the quantum energy scales associated with these fluctuations, captured by gravitational anomalies of quantum field theories. We point out that such anomalous fluctuations naturally occur in the quantum atmosphere of a black hole. Our results reveal that analogous fluctuations are also observable in thermal conductors in flat-space time provided local temperature varies strongly. As a consequence, we establish that the gravitational anomalies manifest themselves naturally in non-linear thermal response of a quantum wire. In addition, we propose a systematic way to identify thermal analogues of black hole's anomalous quantum fluctuations associated to gravitational anomalies. We identify their signatures in propagating energy waves following a thermal quench, as well as in the energy density of heating Floquet states induced by repeated thermal quenches.

中文翻译：

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温度与弯曲时空之间的反常卢廷格等价：从黑洞到热猝灭

基于托尔曼和埃伦菲斯特热有重量的观点，卢廷格在引力场和热传输之间建立了深刻的联系。然而，这种关系不包括在强弯曲时空中变得至关重要的反常量子涨落。在这项工作中，我们重新审视著名的托尔曼-埃伦菲斯特和卢廷格关系，并展示如何将与这些波动相关的量子能量尺度结合起来，这些波动是由量子场论的引力异常捕获的。我们指出，这种反常涨落自然发生在黑洞的量子大气中。我们的结果表明，只要局部温度变化剧烈，在平坦时空的热导体中也可以观察到类似的波动。因此，我们确定引力异常自然地表现在量子线的非线性热响应中。此外，我们提出了一种系统方法来识别与引力异常相关的黑洞异常量子涨落的热类似物。我们识别了它们在热淬灭后传播的能量波中的特征，以及在重复热淬灭引起的加热 Floquet 态的能量密度中的特征。