相关论文: Generalizing the Planck distribution
Through the formulation of his law of thermal emission, Kirchhoff conferred upon blackbody radiation the quality of universality [G.Kirchhoff, Annalen der Physik 109, 275 (1860)]. Consequently, modern physics holds that such radiation is…
Complexity theory embodies some of the hardest, most fundamental and most challenging open problems in modern science. The very term complexity is very elusive, so that the main goal of this theory is to find meaningful quantifiers for it.…
In this study, approximate generalized quantal distribution functions and their applications, which appeared in the literature so far, have been summarized. Making use of the generalized Planck radiation law, which have been obtained by the…
We define a general notion of entropy in elementary, algebraic terms. Based on that, weak forms of a scalar product and a distance measure are derived. We give basic properties of these quantities, generalize the Cauchy-Schwarz inequality,…
It is by now well known that the Boltzmann-Gibbs (BG) entropy $S_{BG}=-k\sum_{i=1}^W p_i \ln p_i$ can be usefully generalized into the entropy $S_q=k (1-\sum_{i=1}^Wp_i^{q}) / (q-1)$ ($q\in \mathcal{R}; S_1=S_{BG}$). Microscopic dynamics…
In this talk I will describe the deep influence Planck had on the development of statistical mechanics. At this end I will first outline the theoretical situation of statistical mechanics before Planck. I will then describe his main…
Physical research looks for clues to quantum properties of the gravitational field. On the basis of the common Schr\"odinger theory, a simple model of the quantization of a Friedmann universe comprising dust and radiation is investigated.…
The standard central limit theorem plays a fundamental role in Boltzmann-Gibbs statistical mechanics. This important physical theory has been generalized \cite{Tsallis1988} in 1988 by using the entropy $S_q = \frac{1-\sum_i p_i^q}{q-1}$…
By numerical calculation, the Planck spectrum with zero-point radiation is shown to satisfy a natural maximum-entropy principle whereas alternative choices of spectra do not. Specifically, if we consider a set of conducting-walled boxes,…
In 1924, Satyendra Nath Bose's pioneering work laid the foundation for Bose-Einstein statistics, which describes particles with integral spins. His derivation of Planck's law for blackbody radiation bypassed classical assumptions, relying…
A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence…
The interplay between optical and statistical physics is a rich and exciting field of study. Black body radiation was the first application of photon statistics, although it was initially treated as a problem of the cavity oscillators in…
The object of this work is to give the key to answer whether or not there is another numerical method which is different from the equation proposed by Planck to predict blackbody radiation by frequency. Firstly, Maxwell distribution…
The cornerstone of Boltzmann-Gibbs ($BG$) statistical mechanics is the Boltzmann-Gibbs-Jaynes-Shannon entropy $S_{BG} \equiv -k\int dx f(x)\ln f(x)$, where $k$ is a positive constant and $f(x)$ a probability density function. This theory…
Planck's law describes the radiation of black bodies. The study of its properties is of special interest, as black bodies are a good description for the behavior of many phenomena. In this work a new mathematical study of Planck's law is…
The nonextensive statistics based on the $q$-entropy $S_q=-\frac{\sum_{i=1}^v(p_i-p_i^q)}{1-q}$ has been so far applied to systems in which the $q$ value is uniformly distributed. For the systems containing different $q$'s, the…
Planck's law of thermal radiation depends on the temperature, $T$, and the emissivity, $\epsilon$, of a body, where emissivity is the coupling of heat to radiation that depends on both phonon-electron nonradiative interactions and…
The non-extensive canonical ensemble theory is reconsidered with the method of Lagrange multipliers by maximizing Tsallis entropy, with the constraint that the normalized term of Tsallis' $q-$average of physical quantities, the sum $\sum…
Planck's law of thermal radiation depends only on the temperature T and emissivity $\varepsilon$. It is one of the most fundamental discoveries about light-matter interaction that led to the development of quantum physics. Another basic…
In two respects Ludwig Boltzmann was a pioneer of quantum mechanics. First because in his statistical interpretation of the second law of thermodynamics he introduced the theory of probability into a fundamental law of physics and thus…