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This paper investigates applicability of thermodynamic concepts and principles to competitive systems. We show that Tsallis entropies are suitable for characterisation of systems with transitive competition when mutations deviate from Gibbs…
We review the ubiquitous presence in multiparticle production processes of quasi-power law distributions (i.e., distributions following pure power laws for large values of the argument but remaining finite, usually exponential, for small…
An algebraic approach to the study of entanglement entropy of quantum systems is reviewed. Starting with a state on a $C^*$-algebra, one can construct a density operator describing the state in the GNS representation state. Applications of…
We give a notion of entropy for general gemetric structures, which generalizes well-known notions of topological entropy of vector fields and geometric entropy of foliations, and which can also be applied to singular objects, e.g. singular…
The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its…
A generalised notion of exponential families is introduced. It is based on the variational principle, borrowed from statistical physics. It is shown that inequivalent generalised entropy functions lead to distinct generalised exponential…
In nonextensive statistical mechanics, two kinds of definitions have been considered for expectation valu of a physical quantity: one is the ordinary definition and the other is the normalized q-expectation value employing the escort…
How complex of the complex networks has attracted many researchers to explore it. The entropy is an useful method to describe the degree of the $complex$ of the complex networks. In this paper, a new method which is based on the Tsallis…
In 1988, Constantino Tsallis proposed an extension of the Boltzmann statistical mechanics by postulating a new entropy formula, $S_q = k_B\ln_q W$, where $W$ is the number of microstates accessible to the system, and $\ln_q$ defines a…
We investigate the cumulative Tsallis entropy, an information measure recently introduced as a cumulative version of the classical Tsallis differential entropy, which is itself a generalization of the Boltzmann-Gibbs statistics. This…
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of…
A three-parameter logarithmic function is derived using the notion of q-analogue and ansatz technique. The derived three-parameter logarithm is shown to be a generalization of the two-parameter logarithmic function of Schwammle and Tsallis…
The Tsallis entropy, which possesses non-extensive property, is derived from the first principle employing the non-extensive Hamiltonian or the $q$-deformed Hamiltonian with the canonical ensemble assumption in statistical mechanics. Here,…
We show that finite systems whose Hamiltonians obey a generalized homogeneity relation rigorously follow the nonextensive thermostatistics of Tsallis. In the thermodynamical limit, however, our results indicate that the Boltzmann-Gibbs…
The entropic form $S_q$ is, for any $q \neq 1$, {\it nonadditive}. Indeed, for two probabilistically independent subsystems, it satisfies $S_q(A+B)/k=[S_q(A)/k]+[S_q(B)/k]+(1-q)[S_q(A)/k][S_q(B)/k] \ne S_q(A)/k+S_q(B)/k$. This form will…
The original canonical ensemble formalism for the nonextensive entropy thermostatistics is reconsidered. It is shown that the unambiguous connection of the statistical mechanics with the equilibrium thermodynamics is provided if the…
We present two issues here: (i) that in situation when total energy is kept constant recently proposed fluctuations of volume ensemble is equivalent to the approach using Tsallis statistics with fluctuating temperature and (ii) that the…
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,…
Behavior of condensed matter systems deviating from the standard equilibrium conditions is discussed. Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the…
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…