Related papers: Some geometrical aspects of the Microcanonical Dis…
We discuss different aspects of the present status of the Statistical Physics focusing the attention on the non-extensive systems, and in particular, on the so called small systems. Multimicrocanonical Distribution and some of its geometric…
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…
In the present paper we continue our reconsideration about the foundations for a thermostatistical description of the called Hamiltonian nonextensive systems (see in cond-mat/0604290). After reviewing the selfsimilarity concept and the…
The main interest of the present work is the generalization of the Boltzmann-Gibbs distributions and the fluctuation theory based on the consideration of the reparametrization invariance of the microcanonical ensemble. This approach allows…
We introduce a modification of the well-known Metropolis importance sampling algorithm by using a methodology inspired on the consideration of the reparametrization invariance of the microcanonical ensemble. The most important feature of…
Legendre invariant metrics have been introduced in Geometrothermodynamics to take into account the important fact that the thermodynamic properties of physical systems do not depend on the choice of thermodynamic potential from a geometric…
A multicanonical formalism is introduced to describe statistical equilibrium of complex systems exhibiting a hierarchy of time and length scales, where the hierarchical structure is described as a set of nested "internal heat reservoirs"…
The reparameterization trick has become one of the most useful tools in the field of variational inference. However, the reparameterization trick is based on the standardization transformation which restricts the scope of application of…
Extended geometric distribution is defined and its mixture is characterized by the property of having completely monotone probability sequence. Also, convolution equations and probability generating functions are used to characterize…
In this paper, we introduce a new generalization of geometric distribution which can also viewed as discrete analogue of weighted exponential distribution introduced by Gupta and Kundu(2009). We study some basic distributional properties…
We develop a generalized theory of (meta)equilibrium statistical mechanics in the thermodynamic limit valid for both smooth and fractal phase spaces. In the former case, our approach leads naturally to Boltzmann-Gibbs standard…
The eigenstate thermalization hypothesis provides a framework for understanding thermalization in isolated quantum many-body systems by characterizing statistical properties of local observables in energy eigenstates. Here we demonstrate…
In the present paper are considered the self-similarity scaling postulates in order to extend the Thermodynamics to the study of one special class of nonextensive systems: the pseudoextensive, those with exponential behavior for the…
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…
In this paper, we consider the volume enclosed by the microcanonical ensemble in phase space as a statistical ensemble. This can be interpreted as an intermediate image between the microcanonical and the canonical pictures. By maintaining…
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…
A conception of inhomogeneous locally random distribution of microdefects in crystalline solids is proposed. A method to calculate some physical properties of solids, containing inhomogeneously distributed defects, is developed. A…
Transmuted geometric distribution with two parameters and is proposed as a new generalization of the geometric distribution by employing the quadratic transmutation techniques of Shaw and Buckley (2007). Its important distributional and…
It is developed a Riemannian reformulation of classical statistical mechanics for systems in thermodynamic equilibrium, which arises as a natural extension of Ruppeiner geometry of thermodynamics. The present proposal leads to interpret…
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…