Pico-canonical ensembles: A theoretical description of metastable states

TL;DR

This paper introduces pico-canonical ensembles to describe metastable and glassy states in statistical mechanics, accounting for non-ergodic behavior and phase space segmentation, with explicit calculations for a 1D lattice gas.

Contribution

It presents a novel theoretical framework for metastable states using pico-canonical ensembles, extending traditional ensembles to non-ergodic, glassy phases.

Findings

Explicit calculation for a 1D lattice gas model.

Demonstration of phase space segmentation below glass temperature.

Framework captures non-ergodic dynamics in metastable states.

Abstract

We define restricted ensembles, called pico-canonical ensembles, for a statistical-mechanical description of the metastable and glassy phases. In this approach, time-evolution is Markovian, with temperature dependent rates. Below a particular glass-temperature, the system is strongly non-ergodic, and the phase space breaks up into a large number of mutually disconnected sectors. Averages are calculated over states within one such sector, and then averaged over sectors. As a soluble example, we calculate these explicitly for a one dimensional lattice gas with nearest neighbor couplings.