Related papers: Statistical Mechanics of systems with long range i…
We introduce a Hamiltonian dynamics for the description of long-range interacting systems in contact with a thermal bath (i.e., in the canonical ensemble). The dynamics confirms statistical mechanics equilibrium predictions for the…
Systems with long range interactions in general are not additive, which can lead to an inequivalence of the microcanonical and canonical ensembles. The microcanonical ensemble may show richer behavior than the canonical one, including…
One-dimensional hard rod gases are explicitly constructed as the limits of discrete systems: exclusion processes involving particles of arbitrary length. Those continuum many-body systems in general do not exhibit the same hydrodynamic…
We present a review of recent work on the statistical mechanics of non equilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and…
Stochastic processes of interacting particles with varying length are relevant e.g. for several biological applications. We try to explore what kind of new physical effects one can expect in such systems. As an example, we extend the…
Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous…
We revisit the dynamics of the one-dimensional self-gravitating sheets models. We show that homogeneous and non-homogeneous states have different ergodic properties. The former is non-ergodic and the one-particle distribution function has a…
On a fine grained scale the Gibbs entropy of an isolated system remains constant throughout its dynamical evolution. This is a consequence of Liouville's theorem for Hamiltonian systems and appears to contradict the second law of…
Infinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the…
We describe a finite inhomogeneous three dimensional system of classical particles which interact through short and (or) long range interactions by means of a simple analytic spin model. The thermodynamic properties of the system are worked…
The dynamics and the thermodynamics of particles/spins interacting via long-range forces display several unusual features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model, a Hamiltonian system of…
Correlations between the parts of a many-body system, and its time dynamics, lie at the heart of sciences, and they can be classical as well as quantum. Quantum correlations are traditionally viewed as constituted out of classical…
In ergodic physical systems, time-averaged quantities converge (for large times) to their ensemble-averaged values. Large deviation theory describes rare events where these time averages differ significantly from the corresponding ensemble…
One of the key objectives in investigating small stochastic systems is the development of micrometer-sized engines and the understanding of their thermodynamics. However, the primary mathematical tool used for this purpose, the overdamped…
We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…
The foundations for a thermo-statistical description of the called non extensive Hamiltonian systems are reconsidered. The relevance of the parametric resonance as a fundamental mechanism of the Hamiltonian chaoticity in those systems with…
We show that fractional exclusion statistics is manifested in general in interacting systems and we discuss the conjecture recently introduced (J. Phys. A: Math. Theor. 40, F1013, 2007), according to which if in a thermodynamic system the…
The behavior of lattice models in which time reversibility is enforced at the level of trajectories (microscopic reversibility) is studied analytically. Conditions for ergodicity breaking are explored, and a few examples of systems…
Lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a…
To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a…