Related papers: Statistical Mechanics of systems with long range i…
The two-body potential of systems with long-range interactions decays at large distances as $V(r)\sim 1/r^\alpha$, with $\alpha\leq d$, where $d$ is the space dimension. Examples are: gravitational systems, two-dimensional hydrodynamics,…
Thermodynamic and dynamical properties of systems with long range pairwise interactions (LRI) which decay as 1/r^{d+\sigma} at large distances r in $d$ dimensions are reviewed in these Notes. Two broad classes of such systems are…
Thermodynamic and dynamical properties of systems with long-range pairwise interactions (LRI), which decay as $1/r^{d+\sigma}$ at large distances $r$ in $d$ dimensions, are reviewed. Two broad classes of such systems are discussed. (i)…
The thermodynamic and dynamical properties of an Ising model with both short range and long range, mean field like, interactions are studied within the microcanonical ensemble. It is found that the relaxation time of thermodynamically…
In recent years, studies of long-range interacting (LRI) systems have taken centre stage in the arena of statistical mechanics and dynamical system studies, due to new theoretical developments involving tools from as diverse a field as…
A new approach to non-extensive thermodynamical systems with non-additive energy and entropy is proposed. The main idea of the paper is based on the statistical matching of the thermodynamical systems with the additive multi-step Markov…
We briefly review some equilibrium and nonequilibrium properties of systems with long-range interactions. Such systems, which are characterized by a potential that weakly decays at large distances, have striking properties at equilibrium,…
We review theoretical results obtained recently in the framework of statistical mechanics to study systems with long range forces. This fundamental and methodological study leads us to consider the different domains of applications in a…
New methods are presented which enables one to analyze the thermodynamics of systems with long-range interactions. Generically, such systems have entropies which are non-extensive, (do not scale with the size of the system). We show how to…
Enhanced experimental capabilities to control nonlocal and power-law decaying interactions are currently fuelling intense research in the domain of quantum many-body physics. Compared to their counterparts with short-ranged interactions,…
In a first part the scope of classical thermodynamics and statistical mechanics is discussed in the broader context of formal dynamical systems, including computer programmes. In this context classical thermodynamics appears as a particular…
A new concept of the available force in long-range interaction complex systems is proposed. The relationship between the available force in different time intervals and the interaction parameters of complex systems is described. It is found…
Systems with long range interactions display some anomalies when its dynamics and thermodynamics are studied below certain conditions. Among these anomalies are the quasi- stationary states, which are exacerbated because of special initial…
We analyse the statistical physics of a two dimensional lattice based gas with long range interactions. The particles interact in a way analogous to Queens on a chess board. The long range nature of the interaction gives the mathematics of…
A Hamiltonian model living in a bounded phase space and with long-range interactions is studied. It is shown, by analytical computations, that there exists an energy interval in which the microcanonical entropy is a decreasing convex…
Systems with long-range (LR) forces, for which the interaction potential decays with the interparticle distance with an exponent smaller than the dimensionality of the embedding space, remain an outstanding challenge to statistical physics.…
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 determine the conditions under which the presence of long-range interactions reduce the energy losses due to defect generation during non-adiabatic evolution, crucial for enhancing the power to efficiency ratio of quantum thermal…
Considering the interactions of two arbitrary particles, we obtain an internal energy expression of the complex system having long-range interactions. Based on the postulate of "equal-probability principle" for all microstates, the…
Systems with long-range interactions (LRI) display unusual thermodynamical and dynamical properties that stem from the non-additive character of the interaction potential. We focus in this work on the lack of relaxation to thermal…