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This is a brief introduction to general relativity, designed for both students and teachers of the subject. While there are many excellent expositions of general relativity, few adequately explain the geometrical meaning of the basic…

General Relativity and Quantum Cosmology · Physics 2015-06-15 John C. Baez , Emory F. Bunn

We construct a new class of phenomenological equations of state for homogeneous matter for use in simulations of hot and dense matter in local thermodynamic equilibrium. We construct a functional form which respects experimental,…

Nuclear Theory · Physics 2019-02-20 Xingfu Du , Andrew W. Steiner , Jeremy W. Holt

We establish three partial differential equation models describing the thermodynamics of the fluid, by combining the energetic variational approach, appropriate constitutive relations, and classical thermodynamics laws. What is more, by…

Analysis of PDEs · Mathematics 2020-11-23 Ning-An Lai , Chun Liu , Andrei Tarfulea

The basic notions of statistical mechanics (microstates, multiplicities) are quite simple, but understanding how the second law arises from these ideas requires working with cumbersomely large numbers. To avoid getting bogged down in…

Physics Education · Physics 2015-02-27 Thomas A. Moore , Daniel V. Schroeder

We show how to extend the concept of heat capacity to nonequilibrium systems. The main idea is to consider the excess heat released by an already dissipative system when slowly changing the environment temperature. We take the framework of…

Statistical Mechanics · Physics 2011-11-15 Eliran Boksenbojm , Christian Maes , Karel Netocny , Jiri Pesek

It is very likely that the quantum description of spacetime is quite different from what we perceive at large scales, $l\gg (G\hbar/c^3)^{1/2}$. The long wave length description of spacetime, based on Einstein's equations, is similar to the…

General Relativity and Quantum Cosmology · Physics 2009-11-10 T. Padmanabhan

It is shown that measured heat capacity depends on the rate of the temperature variation and on the initial state of a system. It is calculated here in the framework of two-level model. Fenomenological approach gives the same results.

Materials Science · Physics 2007-05-23 Yuri Kornyushin

One general consequence of the Nernst theorem is derived, i.e., the various heat capacities of a thermodynamic system under different constraints approach zero as the temperature approaches absolute zero. The temperature dependence of the…

Statistical Mechanics · Physics 2023-03-15 Shanhe Su , Yinghui Zhou , Guozhen Su , Jincan Chen

Ultrafast laser radiation or beams of fast charged particles primarily excite the electronic system of a solid driving the target transiently out of thermal equilibrium. Apart from the nonequilibrium between the electrons and atoms, each…

Other Condensed Matter · Physics 2024-09-04 Nikita Medvedev , Alexander E. Volkov

'Relativistic thermodynamics' should be understood not as a generalization of a non-relativistic theory but as an application of a general thermodynamic framework, neutral as to spacetime setting and allowing arbitrary conserved quantities,…

Statistical Mechanics · Physics 2025-08-06 David Wallace

The temperature of a mechanical body has a kinetic interpretation: it describes the relative motion of particles within the body. Since the relative velocity of two particles is a Lorentz invariant, so is the temperature. In statistical…

Classical Physics · Physics 2019-02-15 Nikodem Popławski

Providing students of introductory thermal physics with a plot of the heat capacities of many low density gases as a function of temperature allows them to look for systematic trends. Specifically, large amounts of heat capacity data allow…

Physics Education · Physics 2023-08-08 J. D. D. Martin

We give a derivation of the Einstein equation for gravity which employs a definition of the local energy density of the gravitational field as a symmetric second rank tensor whose value for each observer gives the trace of the spatial part…

Mathematical Physics · Physics 2008-03-13 Maurice J. Dupre

The Carnot statement of the second law of thermodynamics poses an upper limit on the efficiency of all heat engines. Recently, it has been studied whether generic quantum features such as coherence and quantum entanglement could allow for…

Statistical Mechanics · Physics 2015-10-14 Bartłomiej Gardas , Sebastian Deffner

A number of successful theoretical models of hardness have been developed recently. A thermodynamic model of hardness, which supposes the intrinsic character of correlation between hardness and thermodynamic properties of solids, allows one…

Materials Science · Physics 2018-04-20 V. A. Mukhanov , O. O. Kurakevych , V. L. Solozhenko

In a recent paper (Phys. Rev. E {\bf 104}, 014103 (2021) ) M. Baggioli and A. Zaccone formulate a theoretical description of the specific heat of liquids by using Debye's expression for the specific heat of solids and inserting a density of…

Disordered Systems and Neural Networks · Physics 2022-12-21 Walter Schirmacher , Taras Bryk , Giancarlo Ruocco

The Einstein's mass-energy relation $E=mc^2$ is one of the most fundamental formulae in physics, but it has not been seriously tested by an elaborated experiment, and only some indirect evidences in nuclear reaction suggested that it holds…

High Energy Physics - Theory · Physics 2018-01-09 Ying-Qiu Gu

We consider stationary driven systems in contact with a thermal equilibrium bath. There is a constant (Joule) heat dissipated from the steady system to the environment as long as all parameters are unchanged. As a natural generalization…

Statistical Mechanics · Physics 2020-01-29 Christian Maes , Karel Netocny

Heat capacity of matter is considered to be its most important property because it holds information about system's degrees of freedom as well as the regime in which the system operates, classical or quantum. Heat capacity is well…

Statistical Mechanics · Physics 2012-06-14 Dima Bolmatov , Vadim Brazhkin , Kostya Trachenko

Eigenstate thermalization hypothesis (ETH) is discussed. We show that one common formulation of ETH does not necessarily imply thermalization of an observable of isolated many body quantum system. To get thermalization one has to postulate…

Statistical Mechanics · Physics 2020-02-06 Oleg Inozemcev , Igor Volovich