Statistical Physics and Thermodynamics of Processes in General Relativity
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Statistical Physics and Thermodynamics of Processes in General Relativity A. L. Krugly* Research Institute for System Analyses of the Russian Academy of Sciences, Nakhimovskiy pr. 36, k. 1, Moscow, 117218, Russia Received June 21, 2019; revised September 4, 2019; accepted February 15, 2020
Abstract—A model of a relativistic process as a finite set of elementary events is considered. General properties of statistics of elementary events are considered. The model has the following properties. Any macroscopic property of any process is a consequence of this statistics. The least action principle means that a macroscopic process chooses a variant with maximum probability. A massive particle is a repetitive process. One cycle is a subset of elementary events. A sequence of these subsets forms a world line. The proper time on an interval of a world line is proportional to the number of cycles in this interval. The mass of a particle is the number of elementary events in this process per unit time. The gravitational field is a manifestation of information generated by the processes. Empty space-time doesn’t exist. DOI: 10.1134/S0202289320020073
1. INTRODUCTION A commonly shared view is that relativistic thermodynamics is a phenomenological theory [1]. First of all, this theory considers transformations of thermodynamics quantities in different frames of reference and the dependence of thermodynamics quantities on gravitational fields. Then, a set of new effects is predicted. This is the black hole entropy [2], the Hawking radiation [3], the Unruh effect [4]. These effects can be a consequence of the thermodynamic nature of gravitation. Jacobson considers the Einstein equation as an equation of state [5]. Similar ideas are considered by Padmanabhan [6] and Verlinde [7] (see [8] for reviews). Gravity can be an emergent phenomenon that arises as the limit of some underlying microscopic theory in the same sense as that hydrodynamics emerges from molecular dynamics [9]. Thermodynamics must be a consequence of the statistics of microstates. In this paper, a new approach is introduced. We consider the concept of relativistic microstates for a simple model of a massive neutral spherically symmetric particle and its gravitational field. The least action principle is considered as a consequence of the statistics of microstates. 2. STATISTICAL PHYSICS OF PROCESSES The main model of nonrelativistic statistical physics is a microstate at a moment of time. A macroscopic state is a set of microstates, and the probability *
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of a macroscopic state is a sum of probabilities of microstates. Any macroscopic quantity is some average value. All thermodynamic laws are consequences of this statistics. But in the relativistic case we cannot correctly define such microstates because, in the general case, we cannot define the moment of time for a finite volume of space. Then we have relativistic thermodynamics only as a phenomenological theory. In relativistic theory we consider four-dimensional space-time instead of 3-dimensional sp
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