Protocol Dependence and State Variables in the Force-Moment Ensemble

• Published in: Physical review letters Vol. 122; no. 3; p. 038001
• Main Authors: Bililign, Ephraim S, Kollmer, Jonathan E, Daniels, Karen E
• Format: Journal Article
• Language: English
• Published: United States 25.01.2019
• ISSN: 1079-7114
• DOI: 10.1103/PhysRevLett.122.038001

Stress-based ensembles incorporating temperaturelike variables have been proposed as a route to an equation of state for granular materials. To test the efficacy of this approach, we perform experiments on a two-dimensional photoelastic granular system under three loading conditions: uniaxial compression, biaxial compression, and simple shear. From the interparticle forces, we find that the distributions of the normal component of the coarse-grained force-moment tensor are exponential tailed, while the deviatoric component is Gaussian distributed. This implies that the correct stress-based statistical mechanics conserves both the force-moment tensor and the Maxwell-Cremona force-tiling area. As such, two variables of state arise: the tensorial angoricity (α[over ^]) and a new temperaturelike quantity associated with the force-tile area which we name keramicity (κ). Each quantity is observed to be inversely proportional to the global confining pressure; however, only κ exhibits the protocol independence expected of a state variable, while α[over ^] behaves as a variable of process.