Related papers: Microcanonical equations for the Tsallis entropy
Microcanonical description is characterized by the presence of an internal symmetry closely related with the dynamical origin of this ensemble: the reparametrization invariance. Such symmetry possibilities the development of a non…
Very recently, the validity of the concept of negative temperature has been challenged by several authors since they consider Boltzmann's entropy (that allows negative temperatures) inconsistent from a mathematical and statistical point of…
The Stephani universes that can be interpreted as an ideal gas evolving in local thermal equilibrium are determined. Five classes of thermodynamic schemes are admissible, which give rise to five classes of regular models and three classes…
We reconsider some general aspects about the mean field thermodynamical description of the astrophysical systems based on the microcanonical ensemble. Starting from these basis, we devote a special attention to the analysis of the scaling…
The underlying connection between the degrees of freedom of a system and its nonextensive thermodynamic behavior is addressed. The problem is handled by starting from a thermodynamical system with fractal structure and its analytical…
Firstly, we calculate quantitatively decrease of entropy by the known formulas in the ordering phenomena and nucleation of thermodynamics of microstructure. They show again that a necessary condition of decrease of entropy in isolated…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the $N-$body phase space with the given total energy. Due to Boltzmann's principle,…
Boltzmann's principle S(E,N,V...)=ln W(E,N,V...) allows the interpretation of Statistical Mechanics of a closed system as Pseudo-Riemannian geometry in the space of the conserved parameters E,N,V... (the conserved mechanical parameters in…
We present general and rigorous results showing that the microcanonical and canonical ensembles are equivalent at all three levels of description considered in statistical mechanics - namely, thermodynamics, equilibrium macrostates, and…
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that…
The second Tisza-Callen postulate of equilibrium thermodynamics states that for any system exists a function of the system's extensive parameters, called entropy, defined for all equilibrium states and having the property that the values…
Concepts of everyday use like energy, heat, and temperature have acquired a precise meaning after the development of thermodynamics. Thermodynamics provides the basis for understanding how heat and work are related and with the general…
We develop the argument that the Gibbs-von Neumann entropy is the appropriate statistical mechanical generalisation of the thermodynamic entropy, for macroscopic and microscopic systems, whether in thermal equilibrium or not, as a…
Within Tsallis statistics, a picture is elaborated to address self--similar time series as a thermodynamic system. Thermodynamic--type characteristics relevant to temperature, pressure, entropy, internal and free energies are introduced and…
The entropy of a thermally isolated system should not decrease after a quench or external driving. For a classical system following Hamiltonian dynamics, we show how this statement emerges for a large system in the sense that the extensive…
The equivalence of thermodynamic results in the canonical and the microcanonical ensembles has been questioned in some calculations for spin models with long-range interactions. We show that these claims of inequivalence are related to an…
Within Tsallis' nonextensive statistics, a model is elaborated to address self-similar time series as a thermodynamic system. Thermodynamic-type characteristics relevant to temperature, pressure, entropy, internal and free energies are…
We derive a class of equations of state for a multi-phase thermodynamic system associated with a finite set of order parameters that satisfy an integrable system of hydrodynamic type. As particular examples, we discuss one-phase systems…
Phase transitions of first and second order can easily be distinguished in small systems in the microcanonical ensemble. Configurations of phase coexistence, which are suppressed in the canonical formulation, carry important information…
The dynamical justifications which lie at the basis of an effective Statistical Mechanics for self gravitating systems are formulated, analyzing some among the well known obstacles thought to prevent a rigorous Statistical treatment. It is…