Related papers: Comment on "Typicality for Generalized Microcanoni…
Given physical systems, counting rule for their statistical mechanical descriptions need not be unique, in general. It is shown that this nonuniqueness leads to the existence of various canonical ensemble theories which equally arise from…
Generalizations of the microcanonical and canonical ensembles for paths of Markov processes have been proposed recently to describe the statistical properties of nonequilibrium systems driven in steady states. Here we propose a theory of…
Due to the equivalence of the statistical ensembles thermostatic properties of physical systems with short-range interactions can be calculated in different ensembles leading to the same physics. In particular, the ensemble equivalence…
This paper is a companion article to our previous paper (J. Stat. Phys. 119, 1283 (2005), cond-mat/0408681), which introduced a generalized canonical ensemble obtained by multiplying the usual Boltzmann weight factor $e^{-\beta H}$ of the…
After reviewing some fundamental results derived from the introduction of the generalized Gibbs canonical ensemble, such as the called thermodynamic uncertainty relation, it is described a physical scenario where such a generalized ensemble…
For a macroscopic, isolated quantum system in an unknown pure state, the expectation value of any given observable is shown to hardly deviate from the ensemble average with extremely high probability under generic equilibrium and…
In systems with long-range interactions, since energy is a non-additive quantity, ensemble inequivalence can arise: it is possible that different statistical ensembles lead to different equilibrium descriptions, even in the thermodynamic…
It is shown, that the only reason for possibility of using microcanonical ensemble is that there are probabilistic processes in microworld, that are not described by quantum mechanic. On a simple example it is demonstrated, that canonical…
We discuss a generalized quantum microcanonical ensemble. It describes isolated systems that are not necessarily in an eigenstate of the Hamilton operator. Statistical averages are obtained by a combination of a time average and a maximum…
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…
An argument used to show that certain varieties of nilpotent groups have instances of nontrivial dominions is considered, and generalized. The same is done with the argument used to show that there are nontrivial dominions in the variety of…
We define a class of spaces on which one may generalise the notion of compactness following motivating examples from higher-dimensional number theory. We establish analogues of several well-known topological results (such as Tychonoff's…
A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.
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…
Shortened abstract: Microcanonical equilibrium macrostates are characterized as the solutions of a constrained minimization problem, while canonical equilibrium macrostates are characterized as the solutions of a related, unconstrained…
We demonstrate the convergence of the characteristic polynomial of several random matrix ensembles to a limiting universal function, at the microscopic scale. The random matrix ensembles we treat are classical compact groups and the…
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…
In this article, we prove a representation theorem that any generic line arrangement in the plane over an ordered field which has global cyclicity can be represented isomorphically by a line arrangement with a given set of distinct slopes…
In the present paper the conditions for the validity of the Tsallis' Statistics are analyzed. The same has been done following the analogy with the traditional case: starting from the microcanonical description of the systems and taking…
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…