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We study the real-time dynamics of quantum models with long-range interactions coupled to a heat-bath within the closed-time path-integral formalism. We show that quantum fluctuations depress the transition temperature. In the subcritical…
We examine the non-extensive approach to the statistical mechanics of Hamiltonian systems with $H=T+V$ where $T$ is the classical kinetic energy. Our analysis starts from the basics of the formalism by applying the standard variational…
We consider hydrodynamic limits of interacting particles systems with open boundaries, where the exterior parameters change in a time scale slower than the typical relaxation time scale. The limit deterministic profiles evolve…
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…
We study a distribution of thermal states given by random Hamiltonians with a local structure. We show that the ensemble of thermal states monotonically approaches the unitarily invariant ensemble with decreasing temperature if all…
We define a nonlinear thermodynamical formalism which translates into dynamical system theory the statistical mechanics of generalized mean-field models, extending investigation of the quadratic case by Leplaideur and Watbled. Under…
The method of positive commutators, developed for zero temperature problems over the last twenty years, has been an essential tool in the spectral analysis of Hamiltonians in quantum mechanics. We extend this method to positive…
We investigate the relationship between ground-state (zero-temperature) quantum phase transitions in systems with variable Hamiltonian parameters and classical (temperature-driven) phase transitions in standard thermodynamics. An analogy is…
Non-equilibrium time evolution in isolated many-body quantum systems generally results in thermalization. However, the relaxation process can be very slow, and quasi-stationary non-thermal plateaux are often observed at intermediate times.…
By assuming an appropriate energy composition law between two systems governed by the same non-extensive entropy, we revisit the definitions of temperature and pressure, arising from the zeroth principle of thermodynamics, in a manner…
I consider the non-equilibrium DC transport of electrons through a quantum system with a thermoelectric response. This system may be any nanostructure or molecule modeled by the nonlinear scattering theory which includes Hartree-like…
The recent interest in aspects common to quantum information and condensed matter has prompted a prosperous activity at the border of these disciplines that were far distant until few years ago. Numerous interesting questions have been…
Mutual equilibrium in long-range interacting systems which involve nonadditive energy, is effectively described in terms of entropy with a nonadditive composition rule. As an example, long range Ising model is considered. The generality of…
The self-consistency of a thermodynamical theory for hadronic sys- tems based on the non-extensive statistics is investigated. We show that it is possible to obtain a self-consistent theory according to the asymptotic bootstrap principle if…
Technological and scientific advances have given rise to an era in which coherent quantum-mechanical phenomena can be probed and experimentally-realised over unprecedented timescales in condensed matter physics. In turn, scientific interest…
Do negative absolute temperatures matter physics and specifically Statistical Physics? We provide evidence that we can certainly answer positively to this vexata quaestio. The great majority of models investigated by statistical mechanics…
The laws of thermodynamics provide a clear concept of the temperature for an equilibrium system in the continuum limit. Meanwhile, the equipartition theorem allows one to make a connection between the ensemble average of the kinetic energy…
It is shown that statistical mechanics is applicable to isolated quantum systems with finite numbers of particles, such as complex atoms, atomic clusters, or quantum dots in solids, where the residual two-body interaction is sufficiently…
A generic feature of systems with long-range interactions is the presence of {\it quasi-stationary} states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian Mean Field (HMF) model, we demonstrate that…
Non-extensive thermodynamics was criticized among others by stating that the Zeroth Law cannot be satisfied with non-additive composition rules. In this paper we determine the general functional form of those non-additive composition rules…