# Dynamics and Thermodynamics of Systems with Long-Range Interactions: An Introduction

@article{Dauxois2002DynamicsAT, title={Dynamics and Thermodynamics of Systems with Long-Range Interactions: An Introduction}, author={Thierry Dauxois and Stefano Ruffo and Ennio Arimondo and Martin Wilkens}, journal={arXiv: Statistical Mechanics}, year={2002}, volume={602}, pages={1-19} }

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 trans-disciplinary perspective (astrophysics, nuclear physics, plasmas physics, metallic clusters, hydrodynamics,...) with a special emphasis on Bose-Einstein condensates.

## 70 Citations

### Incomplete equilibrium in long-range interacting systems.

- PhysicsPhysical review letters
- 2006

It is found that the central limit theorem implies the Boltzmann expression in Gibbs' Gamma space, and the nonequilibrium submanifold of Gamma space characterizing the anomalous behavior is identified, and by restricting the BoltZmann-Gibbs approach to this sub manifold the statistical mechanics of the quasistationary states are obtained.

### Thermodynamics of Small Systems

- Physics
- 2008

After an informal review of the basic ideas in thermodynamics and statistical mechanics, I collect sparse observations on the statistical physics of small systems (small N, few degrees of freedom,…

### SYSTEMS OF POINTS WITH COULOMB INTERACTIONS

- PhysicsProceedings of the International Congress of Mathematicians (ICM 2018)
- 2019

Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even…

### Gravitation in the Microcanonical Ensemble: Appropriate Scaling Leading to Extensivity and Thermalization

- Physics
- 2012

We introduce a simple model of hard spheres with gravitational interactions, for which we study a suitable scaling limit. Usual extensive properties are maintained notwithstanding the long range of…

### Thermodynamic analysis of a long-range interacting spin system

- PhysicsModern Physics Letters B
- 2019

A long-range interacting Fermi chain placed in the uniform and the staggered magnetic field is studied via the micro-canonical approach. The relation between the entropy and the energy of the system…

### Anomalous thermodynamics and phase transitions in neutron star matter

- Physics
- 2007

The presence of the long-range Coulomb force in dense stellar matter implies that the total charge cannot be associated with a chemical potential, even if it is a conserved quantity. As a…

### Vlasov dynamics of a non-neutral plasma

- Physics
- 2007

Long-range interactions are known to induce unusual features in physical systems. An example is given by a non-neutral plasmas. Here, we present a kinetic study of the non-neutral plasma trapped in a…

### A solvable model of hard rods with gravitational interactions

- Physics
- 2015

We consider a simple 1D model of hard rods with gravitational interactions. First, we consider the situation where the sytem is enclosed in a box with finite size and we exactly compute the…

### Thermodynamic properties of a long-range interacting Bose system in staggered magnetic field

- PhysicsThe European Physical Journal B
- 2019

Abstract
This paper provides a brief introduction to the thermodynamic properties of long-range interaction Bose systems in the staggered magnetic field by using the microcanonical approach. The…

### Effects of energy extensivity on the quantum phases of long-range interacting systems

- PhysicsPhysical Review B
- 2021

We investigate the ground state properties of one-dimensional hard-core bosons interacting via a variable long-range potential using the density matrix renormalization group. We demonstrate that…

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