Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac Statistics

Assuming that the maximal allowed number of identical particles in state is an integer parameter, q, we derive the statistical weight and analyze the associated equation which defines the statistical distribution. The derived distribution covers Fermi-Dirac and Bose-Einstein ones in the particular cases q = 1 and q -> infinity (n_i/q -> 1), respectively. We show that the derived statistical weight provides a natural combinatorial interpretation of Haldane-Wu fractional exclus...

We generalize the method introduced in J. Phys. A: Math. Gen. 35, 7255 (2002) based on the concept of thermodynamic equivalence and we transform a Fermi system of general density of states into a thermodynamically equivalent Bose system. This consists of mapping configurations of fermions from the original system onto configurations of bosons, the initial and final configurations having the same energy above the many-body ground state energy. In this way we obtain two systems...

The number-theoretical problem of partition of an integer corresponds to $D=2$. This problem obeys the Bose--Eeinstein statistics, where repeated terms are admissible in the partition, and to the Fermi--Dirac statistics, where they are inadmissible. The Hougen--Watson P,Z-diagram shows that this problem splits into two cases: the positive pressure domain corresponds to the Fermi system, and the negative, to the Bose system. This analogy can be applied to the van der Waals the...

We consider the problem of defining free energy and other thermodynamic functions when the entropy is given as a general function of the probablity distribution, including that for non extensive forms. We find that the free energy, which is central to the determination of all other quantities, can be obtained uniquely numerically ebven when it is the root of a transcendental equation. In particular we study the cases for Tsallis form and a new form proposed by us recently. We...

Analytical expressions for Bose-Einstein condensation of an ideal Bose gas analyzed within the strictures of non-extensive, generalized thermostatistics are here obtained.

The partition function for a system of non-interacting $N-$particles can be found by summing over all the states of the system. The classical partition function for an ideal gas differs from Bosonic or Fermionic partition function in the classical regime. Students find it difficult to follow the differences arising out of incorrect counting by the classical partition function by missing out on the indistinguishability of particles and Fermi-Bose statistics. We present a pedag...

Once again the possibility of the existence of particle statistics intermediate between those of Fermi-Dirac and Bose-Einstein surfaces. Here attention is drawn to the fact that some fifteen years ago it was shown that such so-called 'intermediate' statistics correspond to no physical process and the stationary probability distributions of intermediate statistics are not compatible with any mechanism which allows a variation between Fermi-Dirac and Bose-Einstein statistics.

We generalize techniques previously used to compute ground-state properties of one-dimensional noninteracting quantum gases to obtain exact results at finite temperature. We compute the order-n R\'enyi entanglement entropy to all orders in the fugacity in one, two, and three spatial dimensions. In all spatial dimensions, we provide closed-form expressions for its virial expansion up to next-to-leading order. In all of our results, we find explicit volume scaling in the high-t...

Boltzmann's principle is used to select the "most probable" realization (macrostate) of an isolated or closed thermodynamic system, containing a small number of particles ($N \llsp \infty$), for both classical and quantum statistics. The inferred probability distributions provide the means to define intensive variables and construct thermodynamic relationships for small microcanonical systems, which do not satisfy the thermodynamic limit. This is of critical importance to nan...

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 discuss the entropy of a quantum field not only in the flat space-time but also in a curved space-time. It can also be used to compare the entropies in different dimensional space-times. Analytical expressions for the thermodynamic potential...