On the Thermodynamics of Granular Media

TL;DR

This paper develops a thermodynamic framework for granular media, introducing concepts like granular temperature and pressure to describe fluctuations, dissipation, and transitions such as fluidization.

Contribution

It proposes a novel thermodynamic formulation for granular materials, linking fluctuations and dissipation through a pressure-contact volume conjugate pair.

Findings

Defines a granular temperature analogous to thermodynamic temperature.

Introduces pressure and contact volume as conjugate variables in granular ensembles.

Suggests the response function 'dissipativity' as an indicator of fluidization transition.

Abstract

A thermodynamic formulation for moving granular material is proposed. The fluctuations due to the constant flux and dissipation of energy are controlled in a `granular' ensemble by a pressure $\wp$ (`compression') which is conjugate to a contact volume (`contactopy'). The corresponding response function (`dissipativity') describes how dissipation increases with $\wp$ and should serve to identify the fluidization transition and 1/f noise. In the granular ensemble one can consider the granular medium as a gas of elastically colliding particles and define a ``granular'' temperature and other standard thermodynamic quantities. PACS: 05.70, 46.10