Session B2: The Edwards Statistical Mechanics

Numerical calculation of granular entropy: counting the uncountable.

In 1989, Sir Sam Edwards introduced the concept of `granular entropy', defined as the logarithm of the number of distinct packings of N granular particles in a fixed volume V. The proposal was rather controversial but much of the debate was sterile because the granular entropy could not even be computed for systems as small as 20 particles - hardly a good approximation of the thermodynamic limit. In my talk I will describe how granular entropies of much larger systems can now be computed, using a novel algorithm. Interestingly, it turns out the definition of granular entropy will have to be modified to guarantee that granular entropy is extensive.   

Granular statistical mechanics -- Building on the legacy of Sir Sam Edwards

When Sir Sam Edwards laid down the foundations for the statistical mechanics of jammed granular materials he opened a new field in soft condensed matter and many followed. In this presentation we review briefly the Edwards formalism and some of its less discussed consequences. We point out that the formalism is useful for other classes of systems - cellular and porous materials. A certain shortcoming of the original formalism is then discussed and a modification to overcome it is proposed. Finally, a derivation of an equation of state with the new formalism is presented; the equation of state is analogous to the PVT relation for thermal gases, relating the volume, the boundary stress and measures of the structural and stress fluctuations.   

Unifying Suspensions and Inertial Granular flows near Jamming

Observations support that the fluid to solid transition in granular materials is a continuous transition, with diverging length scales and singular flow curves. I will introduce a framework that predict quantitatively scaling exponents near this transition when particles are frictionless. This framework captures both aerial granular flows and over-damped suspensions, phenomena traditionally studied by two distinct communities.\\ \\In this description, the dense fluid phase can be thought as a gas of excitations of the solid phase. Key aspects of the solid entering the description can be obtained by dynamical argument, and imply that the solid is marginally stable. Recent calculations in infinite spatial dimension support however that thermodynamics arguments a la Edwards also capture this marginality.   

Soft active matter : a contemporary example of Edwardsian statistical mechanics

Colonies of swimming bacteria, algae or spermatozoa are examples of active systems composed of interacting units that consume energy and collectively generate motion and mechanical stresses. Due to the anisotropy of their interactions, these active particles can exhibit orientational order at high concentrations and have been called “living liquid crystals". Biology at the cellular and multicellular scale provides numerous examples of these active systems. They provide a novel class of experimentally accessible system far from equilibrium. Their rich collective behaviour includes non-equilibrium phase transitions and pattern formation on mesoscopic scales. Interestingly however, some of the theoretical insights gained from field theories applied to equilibrium soft matter systems can be used to explain aspects of their behaviour, but with a number of surprising new twists. I will describe and summarise recent theoretical results characterising the behaviour of such soft active systems highlighting in particular the effects of their internal dynamics on their macroscopic behaviour.   

Thinking Outside the Sandbox

Theoretical approaches for inherently out-of-equilibrium systems, from granular to live matter, are at the forefront of soft condensed matter physics. Edwards pioneered a statistical mechanics framework to describe jammed particulate materials, which explains the slow compaction of granular materials towards a given density, the reversibility of such experiments, and the equilibration between shaken powders of different types. During my PhD, Edwards's theoretical work inspired me to develop a transparent emulsion system to test the microscopic distributions underlying granular thermodynamics. I will talk about what it was like to have Sir Sam as a PhD adviser and how he uniquely inspired my curiosity to design and build novel materials, which are not random, but assemble via mobile, multiflavored bonds that respond to environmental queues. I will give an overview of this kind of experimentally guided assembly — these results call for new theories of emulsions with programmable architectures.