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Heat engines convert thermal energy into mechanical work both in the classical and quantum regimes. However, quantum theory offers genuine nonclassical forms of energy, different from heat, which so far have not been exploited in cyclic…
We discuss relevant aspects of the exact q-thermostatistical treatment for an ideal Fermi system. The grand canonical exact generalized partition function is given for arbitrary values of the nonextensivity index q, and the ensuing…
We discuss recent results on the relation between the strongly interacting one-dimensional Bose gas and a gas of ideal particles obeying nonmutual generalized exclusion statistics (GES). The thermodynamic properties considered include the…
During the last three decades, non-standard statistics for indistinguishable quantum particles has attracted broad attentions and research interests from many institutions. Among these new types of statistics, the q-deformed Bose and Fermi…
We investigate the conditions under which quantum fluctuations are relevant for the quantitative interpretation of experiments with ultracold Bose gases. This requires to go beyond the description in terms of the Gross-Pitaevskii and…
The problem of the calculation of equilibrium thermodynamic properties and the establishment of statistical-thermodynamically-consistent finite bound-state partition functions in nonideal multi-component plasma systems is revised within the…
A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balanceable quantities. These flows are first…
In this work, improvements are introduced to the current models of the ideal Fermi gas and the ideal Bose gas by incorporating the quantum nature of phase space, which is directly linked to the uncertainty principle. These improved models…
The empirical rule that systems of identical particles always obey either Bose or Fermi statistics is customarily imposed on the theory by adding it to the axioms of nonrelativistic quantum mechanics, with the result that other statistical…
We develop the basis of the two dimensional generalized quantum statistical systems by using results on $r$-generalized Fibonacci sequences. According to the spin value $s$ of the 2d-quasiparticles, we distinguish four classes of quantum…
The interplay of quantum statistics, interactions and temperature is studied within the framework of the bosonic two-component theory with repulsive delta-function interaction in one dimension. We numerically solve the thermodynamic Bethe…
By constructing the super-particle representation of the free boson gas, we propose a new statistics in which the particles are non-exclusive. This statistics can be considered as a generalization of Bose-Einstein's. The possible…
Statistical entropies of a general relativistic ideal gas obeying Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics are calculated in a general axisymmetry space-time of arbitrary dimension. This general formation can be used to…
We discuss the thermodynamics of a gas of free particles obeying Haldane's exclusion statistics, deriving low temperature and low density expansions. For gases with a constant density of states, we derive an exact equation of state and find…
A new class of identical particles which may exhibit both Bose and Fermi statistics with respective probabilities $p_b$ and $p_f$ is introduced. Such an uncertainity may be either an intrinsic property of a particle or can be viewed as an…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
The phenomenological evidence of quantum statistical effects in parton physics is here briefly summarized, and the recent good results obtained by parameterizing the parton distributions in terms of Fermi-Dirac and Bose-Einstein statistical…
A self-consistent field model for a mixture of Bose and Fermi particles is formulated. There is explored in detail the case of a delta-like interaction, for which the thermodynamic functions are obtained, and Bose-Einstein condensation of…
Asymptotic behavior of a class of nonlinear Schr\"odinger equations are studied. Particular cases of 1D weakly focusing and Bose-Einstein condensates are considered. A statistical approach is presented to describe the stationary probability…
Statistical mechanics is one of the most comprehensive theories in physics. From a boiling pot of water to the complex dynamics of quantum many-body systems it provides a successful connection between the microscopic dynamics of atoms and…