Related papers: Generalizing the Planck distribution
Certain fluctuations in particle number at fixed total energy lead exactly to a cut-power law distribution in the one-particle energy, via the induced fluctuations in the phase-space volume ratio. The temperature parameter is expressed…
We discuss carefully the blackbody approximation, stressing what it is (a limit case of radiative transfer), and what it is not (the assumption that the body is perfectly absorbing, i.e. black). Furthermore, we derive the Planck spectrum…
Several approaches were used to proof the assumption that an universal upper bound on the entropy to energy ratio (S/E) exists in bounded systems. In 1981 Jacob D. Bekenstein published his findings that S/E is limited by the effective…
We study the statistical mechanics of the early radiation dominated universe in the context of a generalized uncertainty principle which supports the existence of a minimal length scale. Utilizing the resultant modified thermodynamical…
We study the statistical mechanics for quantum scalar fields under the multi-parameter rotating black hole spacetime in arbitrary D dimensions. The method of analysis is general in the sense that the metric does not depend on the explicit…
We point out that by considering the Hawking-Bekenstein entropy of Schwarzschild black hole horizons as a non-extensive Tsallis entropy, its additive formal logarithm, coinciding with the Renyi entropy, generates an equation of state with…
We trace the evolution of quantization conditions from Planck's introduction of a new fundamental constant (h) in his treatment of blackbody radiation in 1900 to Heisenberg's interpretation of the commutation relations of modern quantum…
Starting from the basic-exponential, a q-deformed version of the exponential function established in the framework of the basic-hypergeometric series, we present a possible formulation of a generalized statistical mechanics. In a…
In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality observing the…
Statistical mechanics is generalized on the basis of an information theory for inexact or incomplete probability distributions. A parameterized normalization is proposed and leads to a nonextensive entropy. The resulting incomplete…
The blackbody theory of Planck played a seminal role in the development of quantum theory at the turn of the past century. A blackbody cavity is generally thought to be a collection of photons in thermal equilibrium; the radiation emitted…
A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical…
We analyze a simple classical Hamiltonian system within the hypothesis of renormalizability and isotropy that essentially led Maxwell to his ubiquitous Gaussian distribution of velocities. We show that the equilibrium-like power-law energy…
We develop an analytical technique to derive explicit forms of thermodynamical quantities within the asymptotic approach to non-extensive quantum distribution functions. Using it, we find an expression for the number of particles in a boson…
In the last decades the theory of large deviations has become a main tool in statistical mechanics especially in the study of non--equilibrium. In a rational reconstruction of the story one must recognize the ideal connection and debt of…
Starting from metric of the general nonextreme stationary axisymmetric black hole in four-dimensional spacetime, both statistical-mechanical and thermodynamical entropies are studied. First, by means of the "brick wall" model in which the…
It is shown that Tsallis' generalized statistics provides a natural frame for the statistical-thermodynamical description of anomalous diffusion. Within this generalized theory, a maximum-entropy formalism makes it possible to derive a…
A generalized Kullback-Leibler relative entropy is introduced starting with the symmetric Jackson derivative of the generalized overlap between two probability distributions. The generalization retains much of the structure possessed by the…
In earlier work, Billey--Konvalinka--Swanson studied the asymptotic distribution of the coefficients of Stanley's $q$-hook length formula, or equivalently the major index on standard tableaux of straight shape and certain skew shapes. We…
Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using the latter to express probabilistic parameters in terms of the thermodynamic quantities, we get a simple unified derivation of the…