On the thermodynamics of granular media

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 $\mathfrak{p}$ (“compression”) which is conjugate to a contact volume (“contactopy”). The corresponding response function (“dissipativity”) describes how dissipation increases with $\mathfrak{p}$ 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