Related papers: Power-law entropies for continuous systems and gen…
Some preliminary evidence suggests the conjecture that the collective behaviour of systems having long-range interactions may be described more effectively by the Tsallis rather than by the Boltzmann/Gibbs/Shannon entropy. To this end, we…
We present the conclusive mathematical structure behind Tsallis statistics. We obtain mainly the following five theoretical results: (i) the one-to-one correspondence between the q-multinomial coefficient and Tsallis entropy, (ii) symmetry…
We want to relate the concepts of entropy and pressure to that of KMS states for $C^*$-Algebras. Several different definitions of entropy are known in our days. The one we describe here is quite natural and extends the usual one for…
We axiomatically characterize the Tsallis entropy of a finite quantum system. In addition, we derive a continuity property of Tsallis entropy. This gives a generalization of the Fannes inequality.
Product probability property, known in the literature as statistical independence, is examined first. Then generalized entropies are introduced, all of which give generalizations to Shannon entropy. It is shown that the nature of the…
General physics approach is applied to analysis of power components in electrical systems under sinusoidal and non-sinusoidal conditions. Physical essence of active, reactive and distorting powers are determinate. It is shown that the all…
A notion of entropy is introduced for causal fermion systems. This entropy is a measure of the state of disorder of a causal fermion system at a given time compared to the vacuum. The definition is given both in the finite and…
The purpose of this note is to argue that degree of nonextensivity as given by Tsallis distribution obtained from maximum entropy principle has a different origin than nonextensivity inferred from pseudo-additive property of Tsallis…
Uncertainty relations emerging from the Tsallis entropy are derived and discussed. In particular we found a positively defined function that saturates the so called entropic inequalities for entropies characterizing the physical states…
This article is a continuation of my paper [arxiv: 1409.1015v2]. R\'enyi and Tsallis entropies are associated to positive linear operators and properties of some functions related to these entropies are investigated.
We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied…
We first show how a new definition of entropy, which is intuitively very simple, as a divergence in cluster-size space, leads to a generalized form that is nonextensive for correlated units, but coincides exactly with the conventional one…
It exists a large class of systems for which the traditional notion of extensivity breaks down. From experimental examples we induce two general hypothesis concerning such systems. In the first the existence of an internal coordinate system…
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper,…
The usual canonical Hamiltonian or Lagrangian formalism of classical mechanics applied to macroscopic systems describes energy conserving adiabatic motion. If irreversible diabatic processes are to be included, then the law of increasing…
Gibbs' theorem, which is originally intended for canonical ensembles with complete statistics has been generalized to open systems with incomplete statistics. As a result of this generalization, it is shown that the stationary equilibrium…
The nonextensive statistical ensembles are revisited for the complex systems with long-range interactions and long-range correlations. An approximation, the value of nonextensive parameter (1-q) is assumed to be very tiny, is adopted for…
We present aspects of the moduli of curve families on a metric measure space which may prove useful in calculating, or in providing bounds to, non-additive entropies having a power-law functional form. We use as paradigmatic cases the…
We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing…
An axiomatic foundation regarding the entropy for complex systems is established. Missing from decades of research was the requirement that entropy must measure the uncertainty at the informational scale of the maximizing distribution,…