Related papers: Generalizing the Planck distribution
Boltzmann-Gibbs statistical mechanics is based on the entropy $S_{BG}=-k \sum_{i=1}^W p_i \ln p_i$. It enables a successful thermal approach of ubiquitous systems, such as those involving short-range interactions, markovian processes, and,…
Within the approach to doubly special relativity (DSR) suggested by Magueijo and Smolin, a new algebraically justified rule of so-called $\kappa$-addition for the energies of identical particles is proposed. This rule permits to introduce…
We study a nonlinear recombination model from population genetics as a combinatorial version of the Kac-Boltzmann equation from kinetic theory. Following Kac's approach, the nonlinear model is approximated by a mean field linear evolution…
An ion-beam compressed by an external electric force is characterized by a unique non-equilibrium distribution function. This is a special case of Tsallis distribution with entropy index q=2, which allows the system to possess appreciably…
The general covariant Fokker-Planck equations associated with the two different versions of covariant Langevin equation in Part I of this series of work are derived, both lead to the same reduced Fokker-Planck equation for the…
We study a symmetric generalization $\mathfrak{p}^{(N)}_k(\eta, \alpha)$ of the binomial distribution recently introduced by Bergeron et al, where $\eta \in [0,1]$ denotes the win probability, and $\alpha$ is a positive parameter. This…
We derive a relativistically covariant (although not manifestly so) equation for the distribution function of particles accelerated at shocks, which applies also to extremely relativistic shocks, and arbitrarily anisotropic particle…
Recently, several authors have tried to extend the usual concepts of thermodynamics and kinetic theory in order to deal with distributions that can be non-Boltzmannian. For dissipative systems described by the canonical ensemble, this leads…
We introduce a simplified version of Connes-Narnhofer-Thirring's quantum dynamical entropy for quantum systems. It quantifies the amount of information gained about the initial condition from continuously monitoring an observable. A nonzero…
On December 14. 1900, Max Planck communicated his derivation of his radiation formula, which he later called ``an act of desperation''. This date is widely recognized as birthday of quantum theory. For Planck it meant the end of his…
The blackbody radiation is analyzed in universes with $D$ spatial dimensions. With the classical electrodynamics suited to the universe in focus and recurring to the hyperspherical coordinates, it is shown that the spectral energy density…
We review the derivation of Planck's Radiation Formula on the light of recent studies in its centenary. We discuss specially the issue of discreteness, Planck's opinion on his discovery, and the critical analysis on the contributions by…
The concept of wavefunction reduction should be introduced to standard quantum mechanics in any physical processes where effective reduction of wavefunction occurs, as well as in the measurement processes. When the overlap is negligible,…
On the base of the Hamilton theory for the time-like photon in isotropic dielectric with refraction index n (S.Antoci, et.al, 2007), we suggest generalization of the Einstein-Plank-Richardson law for the value of the light energy quantum in…
Traditionally, the Planck constant $h$ makes its debut appearance in quantum physics textbooks in the context of the blackbody radiation law and subsequently as a fundamental ingredient of the physics of the photoelectric effect and the…
We study the dispersion relation obtained from the semiclassical loop quantum gravity. This dispersion relation is considered for a photon system at finite temperatures and the changes to the Planck's radiation law, the Wien and Boltzmann…
In this article we formally investigate the impact of twisted space-time on black-body radiation phenomena, i.e. we derive the $\theta$-deformed Planck distribution function as well as we perform its numerical integration to the…
The domain of validity of standard thermodynamics and Boltzmann-Gibbs statistical mechanics is discussed and then formally enlarged in order to hopefully cover a variety of anomalous systems. The generalization concerns {\it nonextensive}…
This paper is devoted to the study of the statistical mechanics of trapped gravitons obtained by 'trapping' a spherical gravitational wave in a box. As a consequence, a discrete spectrum dependent on the Legendre index $\ell$ similar to the…
Twenty years ago, Rovelli proposed that the degeneracy of black hole (i.e. the exponential of the Bekenstein-Hawking entropy) is given by the number of ways the black hole horizon area can be expressed as a sum of unit areas. However, when…