Chaos and relaxation to equilibrium in systems with long-range interactions

Abstract

In the thermodynamic limit, systems with long-range interactions do not relax to equilibrium, but become trapped in nonequilibrium stationary states. For a finite number of particles a nonequilibrium state has a finite lifetime, so that eventually a system will relax to thermodynamic equilibrium. The time that a system remains trapped in a quasistationary state (QSS) scales with the number of particles as Nδ, with δ > 0, and diverges in the thermodynamic limit. In this paper we will explore the role of chaotic dynamics on the time that a system remains trapped in a QSS.We discover that chaos, measured by the Lyapunov exponents, favors faster relaxation to equilibrium. Surprisingly, weak chaos favors faster relaxation than strong chaos.