Emergence of macroscopic temperatures in systems that are not thermodynamical microscopically: towards a thermodynamical description of slow granular rheology

TL;DR

This paper demonstrates that slow granular systems with non-thermal microscopic dynamics can exhibit a well-defined macroscopic temperature, linking it to configurational states and supporting Edwards' compactivity concept.

Contribution

It introduces a framework showing that non-thermal, driven granular systems have a meaningful macroscopic temperature associated with slow degrees of freedom.

Findings

Slow granular systems exhibit a measurable macroscopic temperature.

This temperature relates to the number of stationary configurations.

The framework supports Edwards' compactivity hypothesis.

Abstract

A scenario for systems with slow dynamics is characterised by stating that there are several temperatures coexisting in the sample, with a single temperature shared by all observables at each (widely separate) time-scale. In preparation for the study of granular rheology, we show within this framework that glassy systems with driving and friction that are generic and do not correspond to a thermal bath --- and whose microscopic `fast' motion is hence not thermal --- have a well-defined macroscopic temperature associated to the slow degrees of freedom. This temperature is what a thermometer coupled to the system will measure if tuned to respond to low frequencies, and since it can be related to the number of stationary configurations, it is the formalisation of Edwards' `compactivity' ideas.