Related papers: Microcanonical equations for the Tsallis entropy
Macroscopic thermodynamics of equilibrium is constructed for systems obeying power-law canonical distributions. With this, the connection between macroscopic thermodynamics and microscopic statistical thermodynamics is generalized. This is…
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…
We develop a method using a coarse graining of the energy fluctuations of an equilibrium quantum system which produces simple parameterizations for the behaviour of the system. As an application, we use these methods to gain more…
Ideal gas is the most fundamental and simple system in thermodynamics, which has extensive applications in energy research and engineering. By reviewing the physical concept of ideal gas, it is found that the current understanding of ideal…
Nonadditive Tsallis $q$-statistics has successfully been applied for a plethora of systems in natural sciences and other branches of knowledge. Nevertheless, its foundations have been severely criticised by some authors based on the…
We present a stability analysis of the classical ideal gas in a new theory of nonextensive statistics and use the theory to understand the phenomena of negative specific heat in some self-gravitating systems. The stability analysis is made…
This paper is a natural continuation of a previous one by the author, which was concerned with the foundations of statistical thermodynamics far from equilibrium. One of the problems left open in that paper was the correct definition of…
We consider the micro-canonical ensemble of a classical Hamiltonian dynamical system, the Hamiltonian being parameter dependent and in the possible presence of other first integrals. We describe a thermodynamic formalism in which a 1st law…
We consider the problem of defining free energy and other thermodynamic functions when the entropy is given as a general function of the probablity distribution, including that for non extensive forms. We find that the free energy, which is…
The nonextensive thermodynamic relations are expressed under the assumption of temperature duality, endowing the "physical temperature" and the "Lagrange temperature" in different physical sense. Based on this assumption, two sets of…
Small thermodynamic systems exhibit peculiar behavior different from that observed in long-scale systems. Non-equilibrium processes taking place in those systems are strongly influenced by the presence of fluctuations which can be large.…
The statistical mechanics of a cloud of particles interacting via their gravitational potentials is an old problem which encounters some issues when the traditional Boltzmann-Gibbs statistics is applied. In this article, we consider the…
This work deals with the physical system governed by a Hamiltonian operator, in two-dimensional space, of spinless charged particles subject to a perpendicular magnetic field B, coupled with a harmonic potential in the context of…
We propose a fundamental relation for a classical ideal gas that is valid at all temperatures with remarkable accuracy. All thermodynamical properties of classical ideal gases can be deduced from this relation at arbitrary temperature.
The nonextensive statistics based on Tsallis entropy have been so far used for the systems composed of subsystems having same $q$. The applicability of this statistics to the systems with different $q$'s is still a matter of investigation.…
We develop a geometric foundation of microcanonical thermodynamics in which entropy and its derivatives are determined from the geometry of phase space, rather than being introduced through an a priori ensemble postulate. Once the minimal…
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,…
A new method is proposed for a treatment of ideal quantum gases in the microcanonical ensemble near the thermodynamic limit. The method allows rigorous asymptotic calculations of the average number of particles and particle number…
We derive Tsallis entropy, Sq, from universal thermostat independence and obtain the functional form of the corresponding generalized entropy-probability relation. Our result for finite thermostats interprets thermodynamically the subsystem…
The generalized zeroth law of thermodynamics indicates that the physical temperature in nonextensive statistical mechanics is different from the inverse of the Lagrange multiplier, beta. This leads to modifications of some of thermodynamic…