Related papers: Canonical ensemble in non-extensive statistical me…
We investigate the limiting cases of Tsallis statistics. The viewpoint adopted is not the standard information-theoretic one, where one derives the distribution from a given measure of information. Instead the mechanical approach recently…
The microcanonical ensemble is a natural starting point of statistical mechanics. However, when it comes to perturbation theory in statistical mechanics, traditionally only the canonical and grand canonical ensembles have been used. In this…
We propose a definition of microcanonical and canonical statistical ensembles based on the concept of density of states. This definition applies both to the classical and the quantum case. For the microcanonical case this allows for a…
An updated review [1] of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q-1 (entropic nonextensivity) as a simple and efficient manner to…
Superstatistics is a "statistics" of "canonical-ensemble statistics". In analogy, we consider here a similar theoretical construct, but based upon the microcanonical ensemble. The mixing parameter is not the temperature but the index q…
We show that the configurational probability distribution of a classical gas always belongs to the q-exponential family. Hence, the configurational subsystem is non-extensive in the sense of Tsallis. One of the consequences of this…
The extended gaussian ensemble (EGE) is introduced as a generalization of the canonical ensemble. The new ensemble is a further extension of the Gaussian ensemble introduced by J. H. Hetherington [J. Low Temp. Phys. {\bf 66}, 145 (1987)].…
We study the energy and entropies for $N$ independent harmonic oscillators in the microcanonical and the canonical ensembles in the Tsallis classical and the Tsallis quantum statistics of entropic parameter $q$, where $N$ is the number of…
The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented…
In the field of classical discrete systems, specifically substitutional alloys, this study introduces a stochastic thermodynamic approach to address nonlinearity within a canonical ensemble. This approach establishes a nonlinear…
We develop a regularization of the quantum microcanonical ensemble, called a Gaussian ensemble, which can be used for derivation of the canonical ensemble from microcanonical principles. The derivation differs from the usual methods by…
Ensemble inequivalence, i.e. the possibility of observing different thermodynamic properties depending on the statistical ensemble which describes the system, is one of the hallmarks of long-range physics, which has been demonstrated in…
Superstatistics is a generalization of equilibrium statistical mechanics that describes systems in nonequilibrium steady states. Among the possible superstatistical distributions, the $q$-canonical ensemble (also known as Tsallis'…
We introduce a nonequilibrium grand-canonical ensemble defined by considering the stationary state of a driven system of particles put in contact with a nonequilibrium particle reservoir. At odds with its equilibrium counterpart, or with…
The capabilities of a new approach towards the foundations of Statistical Mechanics are explored. The approach is genuine quantum in the sense that statistical behavior is a consequence of objective quantum uncertainties due to entanglement…
The volume of phase space may grow super-exponentially ("explosively") with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create…
Breaking of ensemble equivalence between the microcanonical ensemble and the canonical ensemble may occur for random graphs whose size tends to infinity, and is signaled by a non-zero specific relative entropy of the two ensembles. In [3]…
In this didactical note I review in depth the rationale for using generalised canonical distributions in quantum statistics. Particular attention is paid to the proper definitions of quantum entropy and quantum relative entropy, as well as…
We present numerical investigations into the question of the validity of the Boltzmann prescription in Statistical Mechanics for large systems, addressing the issue of whether extensivity of energy implies the extensivity of the Boltzmann…
The particle number and energy fluctuations in the system of charged particles are studied in the canonical ensemble for non-zero net values of the conserved charge. In the thermodynamic limit the fluctuations in the canonical ensemble are…