Related papers: The Free Quon Gas Suffers Gibbs' Paradox
We calculate the canonical partition function $Z_N$ for a system of $N$ free particles obeying so-called `quon' statistics where $q$ is real and satisfies $|q|<1$ by using simple counting arguments. We observe that this system is afflicted…
Since the grand partition function $Z_q$ for the so-called $q$-particles (i.e.,\ quons), $q\in(-1,1)$, cannot be computed by using the standard 2nd quantisation technique involving the full Fock space construction for $q=0$, and its…
The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids (or masses, more generally) are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to…
The quantum statistical mechanics of an ideal gas with a general free-particle energy obeying fractional exclusion statistics are systematically investigated in arbitrary dimensions. The pressure relations, the relation between pressure and…
Gibbsian statistical mechanics is extended into the domain of non-negligible {though non-specified} correlations in phase space while respecting the fundamental laws of thermodynamics. The appropriate Gibbsian probability distribution is…
For small thermodynamic systems in contact with a heat bath, we determine the free energy by imposing the following two conditions. First, the quasi-static work in any configuration change is equal to the free energy difference. Second, the…
It is shown that the textbook formula for the pressure of free massless fermions leads to negative values of the probability mass function of the distribution of the system of free massless fermions in the fermion number. The ways to…
Identical classical particles are distinguishable. This distinguishability affects the number of ways W a macrostate can be realized on the micro-level, and from the relation S = k ln W leads to a non-extensive expression for the entropy.…
Gibbs paradox in the context of statistical mechanics addresses the issue of additivity of entropy of mixing gases. The usual discussion attributes the paradoxical situation to classical distinguishability of identical particles and credits…
We study the long range behavior of a gas whose partition function depends on a parameter q and it has been claimed to be a good approximation to the partition function proposed in the formulation of nonextensive statistical mechanics. We…
A master equation with a Lindblad structure is derived, which describes the interaction of a test particle with a macroscopic system and is expressed in terms of the operator valued dynamic structure factor of the system. In the case of a…
This paper is concerned with statistical properties of a gas of $qp$-bosons without interaction. Some thermodynamical functions for such a system in $D$ dimensions are derived. Bose-Einstein condensation is discussed in terms of the…
We derive an equation for the current of particles in energy space; particles are subject to a mean field effective potential that may represent quantum effects. From the assumption that non-interacting particles imply a free diffusion…
Gibbs states are known to play a crucial role in the statistical description of a system with a large number of degrees of freedom. They are expected to be vital also in a quantum gravitational system with many underlying fundamental…
We brief{}ly review the connection between statistical mechanics and thermodynamics. We show that, in order to satisfy thermodynamics and its Legendre transformation mathematical frame, the celebrated Boltzmann-Gibbs~(BG) statistical…
Consistent statistical physical description is given for systems where the elementary excitations are composite objects. Explicit calculational scheme is constructed for the energy density and the total number of thermodynamical degrees of…
The Gibbs paradox of the first kind (GP1) refers to the false increase in entropy which, in statistical mechanics, is calculated from the process of combining two gas systems S1 and S2 consisting of distinguishable particles. Presented in a…
The classical Gibbs paradox concerns the entropy change upon mixing two gases. Whether an observer assigns an entropy increase to the process depends on their ability to distinguish the gases. A resolution is that an "ignorant" observer,…
The statistics of $q$-oscillators, quons and to some extent, of anyons are studied and the basic differences among these objects are pointed out. In particular, the statistical distributions for different bosonic and fermionic…
Emerging of free (or quantum Boltzmann) statistics for a model of quantum particle interacting with quantum field is described in the stochastic limit without dipole approximation. The quantum field is considered in a Gaussian (for example…