Related papers: Statistical ensembles and X-probability
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…
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…
We investigate the relation between various statistical ensembles of finite systems. If ensembles differ at the level of fluctuations of the order parameter, we show that the equations of states can present major differences. A sufficient…
Thermodynamics and its quantum counterpart are traditionally described with statistical ensembles. Canonical typicality has related statistical mechanics for a system to ensembles of global energy eigen- states of system and its environment…
The paper discusses the physical groundlessness of the models used for the derivation of canonical distribution and provides the experimental data demonstrating the incompleteness of quantum mechanics. The possibility of using statistical…
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…
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…
Employing different statistical ensembles may lead to qualitatively different results concerning averages of physical observables on the mesoscopic scale. Here we discuss differences between the canonical and the grandcanonical ensembles…
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…
The standard assumption for the equilibrium microcanonical state in quantum mechanics, that the system must be in one of the energy eigenstates, is weakened so as to allow superpositions of states. The weakened form of the microcanonical…
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 microcanonical ensemble has long been a starting point for the development of thermodynamics from statistical mechanics. However, this approach presents two problems. First, it predicts that the entropy is only defined on a discrete set…
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…
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…
We suggest an extension of the standard concept of statistical ensembles. Namely, we introduce a class of ensembles with extensive quantities fluctuating according to an externally given distribution. As an example the influence of energy…
The probability distributions for charged particle numbers and their densities are derived in statistical ensembles with conservation laws. It is shown that if this limit is properly taken then the canonical and grand canonical ensembles…
The non-extensive statistical mechanics has been used to describe a variety of complex systems. The maximization of entropy, often used to introduce the non-extensive statistical mechanics, is a formal procedure and does not easily leads to…
A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems…
A problem of the equivalence of statistical ensembles is critically analyzed. It is shown, that although different probability distributions of statistical physics have the same behavior in the thermodynamic limit, there are physical…
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…