Related papers: Heat and Gravitation. I. The Action Principle
Previously, the Einstein equation has been described as an equation of state, general relativity as the equilibrium state of gravity, and $f({\cal R})$ gravity as a non-equilibrium one. We apply Eckart's first order thermodynamics to the…
An Equation of State (\textit{EoS}) closes the set of fluid equations. Although an ideal EoS with a constant \textit{adiabatic index} $\Gamma$ is the preferred choice due to its simplistic implementation, many astrophysical fluid…
Although its practical efficiency is unquestionable, it is well known that thermodynamics presents conceptual difficulties from the theoretical point of view. It is shown that the problem comes from an imperfect compatibility between the…
Predicting the stable phase configuration in a liquid-gas system becomes a fundamental challenge when the stratification favored by gravity conflicts with arrangements induced by heat flow, particularly because standard equilibrium…
Transport is one of the most important physical processes in all energy and length scales. Ideal gases and hydrodynamics are, respectively, two opposite limits of transport. Here, we present an unexpected mathematical connection between…
The thermodynamics of an ideal gas enclosed in a box of volume a1 x a2 x a3 at temperature T is considered. The canonical partition function of the system is expressed in terms of complete elliptic integrals of the first kind, whose…
In this article we develop Poincar\'e ideas about a heat balance of ideal gas considered as a collisionless continuous medium. We obtain the theorems on diffusion in nondegenerate completely integrable systems. As a corollary we show that…
Symmetry plays a crucial role in shaping the theories of fundamental forces. For example, general covariance -- the equivalence of all possible coordinate systems of spacetime -- dictates the law of gravity. Here, we extend this concept to…
We investigate how an equation of state for matter is affected when a gravity is present. For this purpose, we consider a box of ideal gas in the presence of Newtonian gravity. In addition to the ordinary thermodynamic quantities, a…
The action principle is introduced to describe the thermodynamic processes of the state functions from the initial equilibrium state to the final equilibrium state. To capture the path-independent property of the state functions through the…
This article mainly consists in the quantum mechanical study of an adiabatically compressed particle, in an infinitely high well, which we conjecture, can be considered as the basis of an ideal gas. Thus we prove that, all the compression…
We study thermodynamics of a heat-conducting ideal gas system. The study is based on i) the first law of thermodynamics from action formulation which expects heat-dependence of energy density and ii) the existence condition of a (local)…
Starting from a formulation for the $dS$ element that includes movement, and considering the variation of the entropy Lorentz invariant, we found the relativistic transformations for thermodynamic systems that satisfy the three laws of…
The topic of this conference is ``The Chaotic Universe''. One of the main achievements of last century has been to relate chaos in fluids to their thermodynamics. It is our purpose to make connection between chaos in gravitation and…
A classical (non-quantum-mechanical) relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated frame of reference is studied using Gibbs's microcanonical and grand canonical formulations of statistical mechanics. Using…
Originally formulated for macroscopic machines, the laws of thermodynamics were recently shown to hold for quantum systems coupled to ideal sources of work (external classical fields) and heat (systems at equilibrium). Ongoing efforts have…
In the present paper, we study the thermodynamics behavior of the field equations for the generalized f(T) gravity with an arbitrary coupling between matter and the torsion scalar. In this regard, we explore the verification of the first…
The most probable state of an infinite self-gravitating gas in the dynamical equilibrium is defined by `gravitational haziness', a parameter representing many-body effects and formally like the temperature in the case of thermal…
Despite its importance in geological sciences, our understanding of interactions between gas and condensed phases (comprising solids and liquids) remains clouded by the fact that, often, only indirect evidence remains for their occurrence.…
We develop a formulation of global thermodynamics for equilibrium systems under the influence of gravity. The free energy for simple fluids is extended to include a dependence on $(T, V, N, mgL)$, where $L$ represents the vertical system…