相关论文: Two-parameter deformations of logarithm, exponenti…
Entropy in thermodynamics is an extensive quantity, whereas standard methods in statistical mechanics give rise to a non-extensive expression for the entropy. This discrepancy is often seen as a sign that basic formulas of statistical…
In classical probability theory, the convergence of empirical frequencies to theoretical probabilities: as captured by the Law of Large Numbers (LLN): is treated as axiomatic and emergent from statistical assumptions such as independence…
We consider some classes of piecewise expanding maps in finite dimensional spaces having invariant probability measures which are absolutely continuous with respect to Lebesgue measure. We derive an entropy formula for such measures and,…
We study an infinite family of one-parameter deformations, so-called $\alpha$-continued fractions, of interval maps associated to distinct triangle Fuchsian groups. In general for such one-parameter deformations, the function giving the…
Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…
Criteria are given that kappa-deformed logarithmic and exponential functions should satisfy. With a pair of such functions one can associate another function, called the deduced logarithmic function. It is shown that generalized…
The Shannon entropy of a random variable has much behaviour analogous to a signed measure. Previous work has explored this connection by defining a signed measure on abstract sets, which are taken to represent the information that different…
We develop a general method for computing logarithmic and log-gamma expectations of distributions. As a result, we derive series expansions and integral representations of the entropy for several fundamental distributions, including the…
The recent generalizations of Boltzmann-Gibbs statistics mathematically relies on the deformed logarithmic and exponential functions defined through some deformation parameters. In the present work, we investigate whether a deformed…
A pedagogical derivation of statistical mechanics from quantum mechanics is provided, by means of open quantum systems. Besides, a new definition of Boltzmann entropy for a quantum closed system is also given to count microstates in a way…
The entropy definition is deduced by means of (re)deriving the generalized non-linear Langevin equation using Zwanzig projector operator formalism. It is shown to be necessarily related to an invariant measure which, in classical mechanics,…
Shannon entropy, a cornerstone of information theory, statistical physics and inference methods, is uniquely identified by the Shannon-Khinchin or Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the study of…
We revisit the derivation of a formula for the $q$-generalised multinomial coefficient rooted in the $q$-deformed algebra, a foundational framework in the study of nonextensive statistics. Previous approximate expressions in the literature…
The statistics of work done on a quantum system can be quantified by the two-point measurement scheme. We show how the Shannon entropy of the work distribution admits a general upper bound depending on the initial diagonal entropy, and a…
Nonequilibrium complex systems are often effectively described by the mixture of different dynamics on different time scales. Superstatistics, which is "statistics of statistics" with two largely separated time scales, offers a consistent…
The axiomatic structure of the $\kappa$-statistcal theory is proven. In addition to the first three standard Khinchin--Shannon axioms of continuity, maximality, and expansibility, two further axioms are identified, namely the self-duality…
We show how generalized Gibbs-Shannon entropies can provide new insights on the statistical properties of texts. The universal distribution of word frequencies (Zipf's law) implies that the generalized entropies, computed at the word level,…
We extend stochastic thermodynamics by relaxing the two assumptions that the Markovian dynamics must be linear and that the equilibrium distribution must be a Boltzmann distribution. We show that if we require the second law to hold when…
We describe an efficient theoretical criterion, suitable for indistinguishable particles to quantify the quantum correlations of any pure two-fermion state, based on the Slater rank concept. It represents the natural generalization of the…
In many applications, the probability density function is subject to experimental errors. In this work the continuos dependence of a class of generalized entropies on the experimental errors is studied. This class includes the C. Shannon,…