The classical-statistical limit of quantum mechanics is studied. It is proved that the limit ~ → 0 is the good limit for the operators algebra but it si not so for the state compact set. In the last case decoherence must be invoked to obtain the classical-statistical limit.

We investigated two different approaches, which can be used to extend the standard quantum statistical mechanics. One is based on fractional calculus, and other considers extension of concept entropy, i.e., Tsallis statistics. reviewed discussed some main properties these approaches thermal Green function formalism perform developments, simultaneously allowing us analyze each case’s dynamics th...

We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to deal with standard optimization methods, such as simulated and quantum annealing, on an equal basis. Consequently, we extend the quantum annealing ...

We start the discussion of the free Bose gas on Robertson-Walker space-times by introducing a new state on the Weyl algebra of the free massive Klein-Gordon eld on Robertson-Walker space-times. This state approximates a thermal equilibrium state and opens the possibility to do quantum statistical mechanics on expanding universes. We explain why this state is believed to be a physically relevant...

In this paper, the Green function theory of quantum many-particle systems recently presented is reworked within the framework of nonextensive statistical mechanics with a new normalized q-expectation values. This reformulation introduces a renormalization of temperature of the earlier theory and a self-consistency condition. The linear response theory is also presented, along with its two-parti...

In the algebraic formulation the thermodynamic pressure, or free energy, of a spin system is a convex continuous function P defined on a Banach space ~3 of translationally invariant interactions. We prove that each tangent functional to the graph of P defines a set of translationally invariant thermodynamic expectation values, l~Iore precisely each tangent functional defines a translationally i...

We develop statistical mechanics and thermodynamics of Bose and Fermi systems in relativistic harmonic oscillator (RHO) confining potential, which may be applicable in quark gluon plasma (QGP), astrophysics, Bose-Einstein condensation (BEC) etc. Detailed study of QGP system is carried out and compared with lattice results. Further, as an application, our equation of state (EoS) of QGP is used t...