Related papers: Groups, non-additive entropy and phase transitions
Within its range of applicability, the Boltzmann equation seems unique in its capacity to accurately describe the transition from almost any initial state to a self-equilibrated thermal state. Using information-theoretic methods to rephrase…
We show that the typical dynamical system sometimes begins to behave like a non-deterministic system with a small classical entropy, and this behavior lasts an extremely long time, until the system starts decreasing entropy. Then again it…
Increasing the number $N$ of elements of a system typically makes the entropy to increase. The question arises on {\it what particular entropic form} we have in mind and {\it how it increases} with $N$. Thermodynamically speaking it makes…
We discuss the dynamics and thermodynamics of systems with weak long-range interactions. Generically, these systems experience a violent collisionless relaxation in the Vlasov regime leading to a (usually) non-Boltzmannian quasi stationary…
A family of nonlinear ordinary differential equations with arbitrary order is obtained by using nonextensive concepts related to the Tsallis entropy. Applications of these equations are given here. In particular, a connection between…
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
We propose a new way of defining entropy of a system, which gives a general form which may be nonextensive as Tsallis entropy, but is linearly dependent on component entropies, like Renyi entropy, which is extensive. This entropy has a…
We propose a formal extension of thermodynamics and kinetic theories to a larger class of entropy functionals. Kinetic equations associated to Boltzmann, Fermi, Bose and Tsallis entropies are recovered as a special case. This formalism…
Taking the nonextensive Tsallis and R\'enyi entropies into account, we explore thermodynamic properties and phase transitions of the Kerr-Newman black holes (KNBH) in the microcanonical and canonical ensembles. We also compare our results…
We show that the non-additivity relation of the Tsallis entropies in nonextensive statistical mechanics has a simple physical interpretation for systems with fluctuating temperature or fluctuating energy dissipation rate. We also show that…
In this paper we develop a generalized formalism for equilibrium thermodynamic systems when an information is shared between the system and the reservoir. The information results in a correction to the entropy of the system. This extension…
Quite general, analytical (both exact and approximate) forms for discrete probability distributions (PD's) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in…
The physical foundations of a variety of emerging technologies --- ranging from the applications of quantum entanglement in quantum information to the applications of nonequilibrium bulk and interface phenomena in microfluidics, biology,…
For a dynamical system far from equilibrium, one has to deal with empirical probabilities defined through time-averages, and the main problem is then how to formulate an appropriate statistical thermodynamics. The common answer is that the…
The nonextensive kinetic theory for degenerate quantum gases is discussed in the general relativistic framework. By incorporating nonadditive modifications in the collisional term of the relativistic Boltzmann equation and entropy current,…
We study the consequences of introducing quantum group invariance in the formalism of nonextensive quantum statistical mechanics. We find that the corresponding thermodynamical system is equivalent to a Bose-Einstein gas in the…
The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic paaroaches based on the principle of equal a priori probability…
The possible distinction between inanimate and living matter has been of interest to humanity since thousands of years. Clearly, such a rich question can not be answered in a single manner, and a plethora of approaches naturally do exist.…
The selection of an equilibrium state by maximising the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of…
A major challenge in the study of active matter lies in quantitative characterization of phases and transitions between them. We show how the entropy of a collection of active objects can be used to classify regimes and spatial patterns in…