Related papers: The Gibbs paradox
The entropy of a spherically symmetric distribution of matter in self-equilibrium is calculated. When gravitational effects are neglected, the entropy of the system is proportional to its volume. As effects due to gravitational…
Solutions to the BBGKY hierarchy of equations for molecular Brownian particle in ideal gas are considered, and exact relations are derived between probability distribution of path of the particle, its derivatives in respect to gas density…
To illustrate Boltzmann's construction of an entropy function that is defined for a microstate of a macroscopic system, we present here the simple example of the free expansion of a one dimensional gas of non-interacting point particles.…
Mounting evidences are being gathered suggesting that income and wealth distribution in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas in equilibrium, but also deviating…
The probability amplitude for $N$ particles in a quantum gas with negligible range of interparticle interaction potentials to come to a small region of size $r$ scales like $r^\gamma$. It is shown that $\gamma$ is quantitatively related to…
An equilibrium theory of classical fluids based on the space distribution among the particles is derived in the framework of the energy minimization method. This study is motivated by current difficulties of evaluation of optical properties…
In this work we investigate the dynamical properties of a mixture of mutually interacting spherical molecules of different masses and sizes. From an analysis of the microscopic laws governing the motion of the molecules we derive a set of…
Comparison of the thermodynamic entropy with Boltzmann's principle shows that under conditions of constant volume the total number of arrangements in simple thermodynamic systems with temperature-independent heat capacities is TC/k. A…
People are well aware that, inherently, certain small-scale nonchaotic particle movements are not governed by thermodynamics. Usually, such phenomena are studied by kinetic theory and their energy properties are considered "trivial". In…
Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles.…
We investigate the splash phenomenon resulting from the energy input at the interface between a vacuum and an inhomogeneous gas with density profile $\rho(r) = \rho_0 r^{-\beta}$. The energy input causes the formation of ballistic spatters…
Collisionless plasmas exhibit nonthermal particle distributions after being energized; as a consequence, they enter a state of low Boltzmann-Gibbs (BG) entropy relative to the thermal state. The Vlasov equations predict that in a…
We discuss the equivalence between kinetic wealth-exchange models, in which agents exchange wealth during trades, and mechanical models of particles, exchanging energy during collisions. The universality of the underlying dynamics is shown…
We discuss the influence of collisions on the dynamics of an ultracold gas whose constituents interact via dipolar forces. This dynamics is governed by the elastic scattering cross section of the molecules, which is to some extent under the…
We present an example counter to the widely-accepted concept on equilibrium states that "Any thermodynamic equilibrium state of two component systems is determined by specifying 4 thermodynamic variables that include at least 1 extensive…
We theoretically investigate the effects of atom losses in the one-dimensional (1D) Bose gas with repulsive contact interactions, a famous quantum integrable system also known as the Lieb-Liniger gas. The generic case of K-body losses (K =…
Entropy of all systems that we understand well is proportional to their volumes except for black holes given by their horizon area. This makes the microstates of any quantum theory of gravity drastically different from the ordinary matter.…
Gravitational and hydrodynamical perturbations are analysed in a relativistic plasma containing a mixture of interacting fluids characterized by a non-negligible bulk viscosity coefficient. The energy-momentum transfer between the…
A finite dimensional-system whose physics is governed by a Gaussian distribution can be regarded as a subsystem of an infinite dimensional-underlying system described by a uniform distribution on the (infinite dimensional) sphere. In turn,…
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…