Thermodynamics and dynamics of systems with long-range interactions

TL;DR

This paper reviews the thermodynamic and dynamical behaviors of systems with long-range interactions, highlighting their unique properties, classifications, and effects near phase transitions and in non-equilibrium steady states.

Contribution

It provides a comprehensive classification of long-range interacting systems and discusses their unusual thermodynamic and dynamical properties, including ensemble inequivalence and ergodicity breaking.

Findings

Strong LRI systems exhibit negative specific heat and slow correlation decay.

Faster decaying interactions lead to additive energies with less dramatic effects.

Long-range correlations influence phase transition behavior and non-equilibrium steady states.

Abstract

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) Systems with a slow decay of the interactions, termed "strong" LRI, where the energy is super-extensive. These systems are characterized by unusual properties such as inequivalence of ensembles, negative specific heat, slow decay of correlations, anomalous diffusion and ergodicity breaking. (ii) Systems with faster decay of the interaction potential, where the energy is additive, thus resulting in less dramatic effects. These interactions affect the thermodynamic behavior of systems near phase transitions, where long-range correlations are naturally present. Long-range correlations are often present in systems driven out of equilibrium when the dynamics involves conserved quantities. Steady state properties of driven systems with local dynamics are considered within the framework outlined above.