Statistical theory of quasi stationary states beyond the single water-bag case study

TL;DR

This paper extends the statistical theory of quasi-stationary states in the Hamiltonian Mean Field model to multiple water-bag initial conditions, demonstrating excellent agreement with microcanonical simulations for two-level water-bags.

Contribution

It generalizes the maximum entropy approach to arbitrary overlapping water-bag initial conditions beyond the single water-bag case.

Findings

Excellent agreement with microcanonical simulations for two-level water-bag initial states.

The extended theory accurately predicts out-of-equilibrium quasi-stationary states.

Validation of the generalized approach for complex initial conditions.

Abstract

An analytical solution for the out-of-equilibrium quasi-stationary states of the paradigmatic Hamiltonian Mean Field (HMF) model can be obtained from a maximum entropy principle. The theory has been so far tested with reference to a specific class of initial condition, the so called (single-level) water-bag type. In this paper a step forward is taken by considering an arbitrary number of overlapping water bags. The theory is benchmarked to direct microcanonical simulations performed for the case of a two-levels water-bag. The comparison is shown to return an excellent agreement.