Related papers: Canonical ensemble in non-extensive statistical me…
Entropy in thermodynamics is an extensive quantity, whereas standard methods in statistical mechanics give rise to a non-extensive expression for the entropy. This discrepancy is often seen as a sign that basic formulas of statistical…
The non-extensive statistical mechanics has been applied to describe a variety of complex systems with inherent correlations and feedback loops. Here we present a dynamical model based on previously proposed static model exhibiting in the…
In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity…
Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. When studying these type of systems with the standard textbook…
A new statistical ensemble is examined using the example of classical one-component simple fluid. It's logical to call it an open ensemble, because its peculiarity is the inclusion in the consideration some surrounding area. Calculations…
It is shown by simple and straightforward considerations that discreteness of basic physical variables is, at least, essential for generalized statistical mechanics with non-logarithmic entropy to be thermodynamically applicable to…
The phenomenon of partial equivalence of statistical ensembles is illustrated by discussing two examples, the mean-field XY and the mean-field spherical model. The configurational parts of these systems exhibit partial equivalence of the…
Non-extensive systems do not allow to go to the thermodynamic limit. Therefore we have to reformulate statistical mechanics without invoking the thermodynamical limit. I.e. we have to go back to Pre-Gibbsian times. We show that Boltzmann's…
In the realm of statistical mechanics, it has been established that there is no distinction between the micro-canonical and canonical ensembles in the thermodynamic limit. However, this paradigm may alter when addressing statistical…
A quantum microcanonical postulate is proposed as a basis for the equilibrium properties of small quantum systems. Expressions for the corresponding density of states are derived, and are used to establish the existence of phase transitions…
Devising a statistical mechanics framework for jammed granular materials is a challenging task as those systems do not share some important properties required to characterize them with statistical thermodynamics tools. In a recent paper…
Polydisperse systems are commonly encountered when dealing with soft matter in general or any non simple fluid. Yet their treatment within the framework of statistical thermodynamics is a delicate task as the latter has been essentially…
A Hamiltonian model living in a bounded phase space and with long-range interactions is studied. It is shown, by analytical computations, that there exists an energy interval in which the microcanonical entropy is a decreasing convex…
It is well-known that the entropy of the microcanonical ensemble cannot be calculated as the Legendre transform of the canonical free energy when the entropy is nonconcave. To circumvent this problem, a generalization of the canonical…
In the case of a system with an unbounded hamiltonian the entropic index q of non-extensive thermodynamics has an upperbound q_c>1 beyond which the formalism becomes meaningless. The expression 1/(q_c-1) is the dimension of the state space…
We propose a new approach to justify the use of the microcanonical ensemble for isolated macroscopic quantum systems. Since there are huge number of independent observables in a macroscopic system, we cannot see all of them. Actually what…
Introduced by Boltzmann under the name "monode," the microcanonical ensemble serves as the fundamental representation of equilibrium thermodynamics in statistical mechanics by counting all possible realizations of a system's states.…
For non-equilibrium systems in a steady state we present two necessary and sufficient conditions for the emergence of $q$-canonical ensembles, also known as Tsallis statistics. These conditions are invariance requirements over the…
We investigate different measures of stability of quantum statistical ensembles with respect to local measurements. We call a quantum statistical ensemble "stable" if a small number of local measurements cannot significantly modify the…
We study the statistical mechanics of classical and quantum systems in non-equilibrium steady states. Emphasis is placed on systems in strong thermal gradients. Various measures and functional forms of observables are presented. The quantum…