Equilibrium statistical mechanics is built on thermal fluctuations and energy conservation. Many systems of current interest, however, including granular materials, dense suspensions, and amorphous solids, are essentially athermal, with dynamics governed instead by mechanical constraints, external driving, and dissipation.
This course provides an introduction to the statistical physics of athermal matter, focusing on how microscopic constraints give rise to macroscopic mechanical behavior. We begin with the jamming transition, isostaticity, and marginal stability, before discussing the vibrational spectrum of amorphous solids, soft modes, and the emergence of anomalous elasticity. We then examine the scaling of elastic moduli, long-range stress correlations, and continuum descriptions of disordered solids. Finally, we turn to dynamics, including yielding, plasticity, dense suspension rheology, and hydrodynamic descriptions of flowing athermal systems, highlighting some of the central open problems in the field.
