相关论文: Pathway Model, Superstatistics, Tsallis Statistics…
We prove that Sharma-Mittal entropy is a subadditive and supermodular function on the lattice of all $n$-dimensional probability distributions, ordered according to the partial order relation defined by majorization among vectors. Our…
This work deals with the scattering entropy of quantum graphs in many different circumstances. We first consider the case of the Shannon entropy and then the R\'enyi and Tsallis entropies, which are more adequate to study distinct…
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…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
For certain families of finite quantum graphs, we study the question of how eigenfunctions are distributed over the graph. To characterize properties of the distribution, generalized entropies of the R\'{e}nyi and Tsallis types are…
This paper introduces a comprehensive extension of the path integral formalism to model stochastic processes with arbitrary multiplicative noise. To do so, It\^o diffusive process is generalized by incorporating a multiplicative noise term…
We show that if one uses the invariant form of the Boltzmann-Shannon continuous entropy, it is possible to obtain the generalized Pareto-Tsallis density function, using an appropriate "prior" measure m_{q}(x) and a "Boltzman constraint"…
In order to study as a whole a wide part of entropy measures, we introduce a two-parameter non-extensive entropic form with respect to the $h$-derivative, which generalizes the conventional Newton--Leibniz calculus. This new entropy,…
We present a new approach to far-from-equilibrium statistical mechanics, based on the concept of generalized entropy, which is a microscopically-defined generalization of Onsager-Machlup functional. In the case when a set of slow…
Superstatistics are superpositions of different statistics relevant for driven nonequilibrium systems with spatiotemporal inhomogeneities of an intensive variable (e.g., the inverse temperature). They contain Tsallis statistics as a special…
We show that starting with either the non-extensive Tsallis entropy in Wang's formalism or the extensive Renyi entropy, it is possible to construct the equilibrium statistical mechanics with non-Gibbs canonical distribution functions. The…
The entropy shows an unavoidable tendency of disorder in thermostatistics according to the second thermodynamics law. This provides a minimization entropy principle for quantum thermostatistics with the von Neumann entropy and nonextensive…
The asymptotic correspondence between the probability mass function of the $q$-deformed multinomial distribution and the $q$-generalised Kullback-Leibler divergence, also known as Tsallis relative entropy, is established. The probability…
We provide a unifying axiomatics for Renyi's entropy and non-extensive entropy of Tsallis. It is shown that the resulting entropy coincides with Csiszar's measure of directed divergence known from communication theory.
We conclude a sequence of work by giving near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves on prior results that obtain…
The development of high-performance solid-state electrolytes (SSEs) has entered a critical stage, where entropy-driven strategies offer transformative potential for enhancing electrochemical properties. By engineering local environments for…
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized dimensions, and multifractal spectra. It is shown that with…
We show, in two different ways, that the Tsallis' partition function and its derivatives are related to thermodynamic quantities such as entropy, internal energy, etc., in the same way as in Boltzmann-Gibbs' formalism, with the Lagrange…
We show that in the continuum limit, the average spectrum method (ASM) is equivalent to maximizing R\'enyi entropies of order $\eta$, of which Shannon entropy is the special case $\eta=1$. The order of R\'enyi entropy is determined by the…
The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral one…