Related papers: Transport Equation for Small Systems and Nonadditi…
We have discussed dynamical properties of the Tsallis entropy and the generalized Fisher information in nonextensive systems described by the Langevin model subjected to additive and multiplicative noise. Analytical expressions for the…
We propose a novel approach in the study of transport phenomena in dense systems or systems with long range interactions where multiple particle interactions must be taken into consideration. Within Boltzmann's kinetic formalism, we study…
Nonadditive composition rules for several physical quantities are treated in thermodynamics. It is argued that the zeroth law defines the existence of their additive forms, the formal logarithms. A further principle, the universal…
Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous…
Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological, and social processes. The…
In recent years, the study of biological transportation networks has attracted significant interest, focusing on their self-regulating, demand-driven nature. This paper examines a mathematical model for these networks, featuring nonlinear…
The non-Markoffian transport equations for the systems of cold Bose atoms confined by a external potential both without and with a Bose-Einstein condensate are derived in the framework of nonequilibrium thermal filed theory (Thermo Field…
More and more works deal with statistical systems far from equilibrium, dominated by unidirectional stochastic processes augmented by rare resets. We analyze the construction of the entropic distance measure appropriate for such dynamics.…
G\"oran Lindblad in 1983 published a monograph on non-equilibrium thermodynamics. We here summarize the contents of this book, and provide a perspective on its relation to later developments in statistical physics and quantum physics. We…
We show that the stochastic interpretation of Tsallis' thermostatistics given recently by Beck [Phys. Rev. Lett {\bf 87}, 180601 (2001)] leads naturally to a multi-parameter generalization. The resulting class of distributions is able to…
In these notes we present some recent results concerning the non-uniqueness of solutions to the transport equation, obtained in collaboration with Gabriel Sattig and Laszlo Szekelyhidi.
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…
Presently, the main methods for describing a non-equilibrium charge-transporting steady state are based on time-evolving it from the initial zero-current situation. An alternative class of theories would give the statistical non-equilibrium…
A new approach to non-extensive thermodynamical systems with non-additive energy and entropy is proposed. The main idea of the paper is based on the statistical matching of the thermodynamical systems with the additive multi-step Markov…
The thermodynamic stability conditions (TSC) of nonadditive and composable entropies are discussed. Generally the concavity of a nonadditive entropy with respect to internal energy is not necessarily equivalent to the corresponding TSC. It…
In this paper we introduce an easy to compute upper bound on the Tsallis entropy of a density matrix describing a system coupled to a noise source. This suggests that the Tsallis entropy is most natural in the context of quantum information…
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…
The role played by non extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics has been discussed in details in many works and…
We extend Onsager's minimum dissipation principle to stationary states that are only subject to local equilibrium constraints, even when the transport coefficients depend on the thermodynamic forces. Crucial to this generalization is a…
The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are…