Related papers: Archimedes' principle for ideal gas
We present the basic mathematical elements of geometrothermodynamics which is a formalism developed to describe in an invariant way the thermodynamic properties of a given thermodynamic system in terms of geometric structures. First, in…
The study considers advantages of the introduced measure of time based on the entropy change under irreversible processes (entropy production). Using the example of non-equilibrium expansion of an ideal gas in vacuum, such a measure is…
We investigate the shape of critical points for a free energy consisting of a nonlocal perimeter plus a nonlocal repulsive term. In particular, we prove that a volume-constrained critical point is necessarily a ball if its volume is…
The accretion of a phantom fluid with non-zero chemical potential by black holes is discussed with basis on the Generalized Second Law of thermodynamics. For phantom fluids with positive temperature and negative chemical potential we…
We undertake a first-principles analysis of the thermodynamics of a small body near a black hole horizon. In particular, we study the paradigmatic system of a quantum ideal gas in a small box hovering over the Schwarzschild horizon. We…
We analyze the Casimir forces for an ideal Bose gas enclosed between two infinite parallel walls separated by the distance D. The walls are characterized by the Dirichlet boundary conditions. We show that if the thermodynamic state with…
For the ideal Fermi gas that fills a quantum well confined by two parallel planes, there are calculated the thermodynamic characteristics in general form for arbitrary temperatures, namely: the thermodynamic potential, energy, entropy,…
We consider non-relativistic electrons in one dimension with infinitely strong repulsive delta function interaction. We calculate the long-time, large-distance asymptotics of field-field correlators in the gas phase. The gas phase at low…
This first article of a series formulates the thermodynamics of ideal gases in a constant gravitational field in terms of an action principle that is closely integrated with thermodynamics. The theory, in its simplest form, does not deviate…
The Gr\"uneisen ratio ($\Gamma$), i.e.\,the ratio of the linear thermal expansivity to the specific heat at constant pressure, quantifies the degree of anharmonicity of the potential governing the physical properties of a system. While…
Collections of self-propelled particles that move persistently by continuously consuming free energy are a paradigmatic example of active matter. In these systems, unlike Brownian "hot colloids", the breakdown of detailed balance yields a…
We show that the self-gravitating gas at thermal equilibrium has an infinite volume limit in the three ensembles (GCE, CE, MCE) when (N, V) -> infty, keeping N/V^{1/3} fixed, that is, with eta = G m^2 N/[ V^{1/3} T] fixed. We develop…
Evading the Mermin-Wagner-Hohenberg no-go theorem and revisiting with rigor the ideal Bose gas confined in a square box, we explore a discrete phase transition in two spatial dimensions. Through both analytic and numerical methods we verify…
Proof of a simple mathematical inequality using elements of surface tension theory and ideal gas law to the formation and coalescence of bubbles.
The non-relativistic self-gravitating gas in thermal equilibrium in the presence of a positive cosmological constant Lambda (dark energy) is investigated. The dark energy introduces a force pushing outward all particles with strength…
The difficulties with which the concept of point-like particles is beset, such as the infinities encountered in the existing theories of elementary particles, suggest a different approach to the study of these particles. Instead of…
A refinement of an argument due to Maxwell for the equipartition of kinetic energy in a mixture of ideal gases with different masses is proposed. The argument is elementary, yet it may work as an illustration of the role of symmetry and…
I develop simple thermodynamic relations for a collection of noninteracting classical particles confined in a harmonic trap. The volume of such a trap is not a good thermodynamic variable, so conventional expressions of the first law of…
We use the notion of intrinsic flat distance to address the almost rigidity of the positive mass theorem for asymptotically hyperbolic manifolds. In particular, we prove that a sequence of spherically symmetric asymptotically hyperbolic…
The standard theory of ideal gases ignores the interaction of the gas particles with the thermal radiation (photon gas) that fills the otherwise vacuum space between them. This is an unphysical feature of the theory since every material in…