A description of the jamming transition in soft particulate matter (Vol. 41, No. 6)

This paper illustrates how the tools of equilibrium statistical mechanics can help explain a different set of natural phenomena-- the physics of systems far-from-equilibrium, such as the jamming transition in granular matter. When S. F. Edwards from Cambridge University proposed a thermodynamic formulation for grains, the community of statistical physics received it as attractive and innovative. However, since there are no first principle justifications of Edwards’s ideas they were also viewed with some degree of scepticism. Since the publication of Edwards’ original work over 20 years ago, the scientific community has debated the possibility of its validity.

Edwards’ ideas consist of proposing a statistical ensemble of volume and stress fluctuations through the thermodynamic notion of entropy, compactivity and angoricity (two temperature-like variables). We find that Edwards’ thermodynamics correctly describes our numerical and theoretical study of the jamming transition (J-point).

Using the ensemble formalism we elucidate two questions regarding the jamming transition: (i) The thermodynamic approach predicts the order of the jamming phase transition by showing the absence of critical fluctuations at jamming in observables like pressure and volume. (ii) We also show that the thermodynamic viewpoint allows one to calculate the physical observables near jamming providing a characterization of jammed solids at the J-Point.

The fact that a simple set of thermodynamics postulates gives rise to the correct results for the case of granular materials driven through the jamming transition may have implications in other fields where out of equilibrium systems are the norm.

Angoricity and compactivity describe the jamming transition in soft particulate matter
Kun Wang, Chaoming Song, Ping Wang and H.A. Makse, EPL, 91, 68001 (2010)