Livadiotis George, McComas David J
Department of Astrophysical Sciences, Princeton University, Princeton, NJ, 08544, USA.
Sci Rep. 2024 Sep 30;14(1):22641. doi: 10.1038/s41598-024-72779-0.
We introduce the theory of thermodynamic relativity, a unified theoretical framework for describing both entropies and velocities, and their respective physical disciplines of thermodynamics and kinematics, which share a surprisingly identical description with relativity. This is the first study to generalize relativity in a thermodynamic context, leading naturally to anisotropic and nonlinear adaptations of relativity; thermodynamic relativity constitutes a new path of generalization, as compared to the "traditional" passage from special to general theory based on curved spacetime. We show that entropy and velocity are characterized by three identical postulates, which provide the basis of a broader framework of relativity: (1) no privileged reference frame with zero value; (2) existence of an invariant and fixed value for all reference frames; and (3) existence of stationarity. The postulates lead to a unique way of addition for entropies and for velocities, called kappa-addition. We develop a systematic method of constructing a generalized framework of the theory of relativity, based on the kappa-addition formulation, which is fully consistent with both thermodynamics and kinematics. We call this novel and unified theoretical framework for simultaneously describing entropy and velocity "thermodynamic relativity". From the generality of the kappa-addition formulation, we focus on the cases corresponding to linear adaptations of special relativity. Then, we show how the developed thermodynamic relativity leads to the addition of entropies in nonextensive thermodynamics and the addition of velocities in Einstein's isotropic special relativity, as in two extreme cases, while intermediate cases correspond to a possible anisotropic adaptation of relativity. Using thermodynamic relativity for velocities, we start from the kappa-addition of velocities and construct the basic formulations of the linear anisotropic special relativity; e.g., the asymmetric Lorentz transformation, the nondiagonal metric, and the energy-momentum-velocity relationships. Then, we discuss the physical consequences of the possible anisotropy in known relativistic effects, such as, (i) matter-antimatter asymmetry, (ii) time dilation, and (iii) Doppler effect, and show how these might be used to detect and quantify a potential anisotropy.
我们介绍了热力学相对论理论，这是一个用于描述熵和速度及其各自的热力学和运动学物理学科的统一理论框架，它们与相对论有着惊人的相同描述。这是首次在热力学背景下对相对论进行推广的研究，自然地导致了相对论的各向异性和非线性适应；与基于弯曲时空从狭义相对论到广义相对论的“传统”路径相比，热力学相对论构成了一条新的推广路径。我们表明，熵和速度由三个相同的假设来表征，这些假设为更广泛的相对论框架提供了基础：（1）不存在具有零值的特权参考系；（2）所有参考系都存在一个不变的固定值；（3）存在平稳性。这些假设导致了一种独特的熵和速度相加方式，称为κ相加。我们基于κ相加公式开发了一种构建相对论理论广义框架的系统方法，该方法与热力学和运动学完全一致。我们将这个同时描述熵和速度的新颖统一理论框架称为“热力学相对论”。从κ相加公式的一般性出发，我们关注与狭义相对论线性适应相对应的情况。然后，我们展示了所发展的热力学相对论如何在两种极端情况下导致非广延热力学中熵的相加以及爱因斯坦各向同性狭义相对论中速度的相加，而中间情况对应于相对论可能的各向异性适应。利用速度的热力学相对论，我们从速度的κ相加开始，构建线性各向异性狭义相对论的基本公式；例如，非对称洛伦兹变换、非对角度规以及能量 - 动量 - 速度关系。然后，我们讨论了已知相对论效应中可能的各向异性的物理后果，例如，（i）物质 - 反物质不对称，（ii）时间膨胀，以及（iii）多普勒效应，并展示了如何利用这些来检测和量化潜在的各向异性。
