## Thermodynamic Analogies in Granular Materials

[source] We used molecular dynamics simulations to investigate energy distributions and spatial clustering in granular gases. Scaling arguments and mean-field calculations we performed for the granular temperature in these systems helped us gain insight on the nature of energy flow in more general driven dissipative systems. We then introduced a solvable stochastic model for dissipative interactions in generic systems, including granular materials, foams, colloidal suspensions and bacterial baths.

We solved the non-Boltzmann energy distribution and demonstrated the variance between different effective temperatures and the violation of time-dependent fluctuation-dissipation relations. By considering distributions in possible phase spaces we showed that an allegedly non-equilibrium model presented by Bertin, Dauchot & Droz is in fact in equilibrium.

In the Maxwell model for driven granular gases, where all grains are equally likely to collide with each other, we showed that time dependent fluctuation-dissipation relations exactly hold in any spatial dimension. For actual dilute gases, where the collision rate is proportional to the relative velocity of each pair of particles, we connected a previously established result concerning the long time limit with analysis we performed for the short time limit in order to show that the ratio of correlation to response depends weakly on the measurement time-scale.

In order to understand what happens when systems in steady states far from thermodynamic equilibrium are connected, we suggested dynamics that dissipate energy locally but conserve it globally. We demonstrated that entropy does not necessarily increase due to contact between systems, and that it may in fact decrease when the macroscopic constraint separating the systems is removed. We found that several commonly used definitions of effective temperatures do not describe the dynamics, since none of them tends to equalize across different systems in contact. We identified the operational temperature of these systems, which controls energy flow until equalizing in the mutual steady state the systems reach, and does not depend on the contact details but only on each systemâ€™s properties. During the investigation of such isolated non-equilibrium systems we also showed how the irreversibility of the dynamics brings about net probability currents and detailed-balance violation, as well as ergodicity breaking in the form of dynamically inaccessible states.

During my PhD I also investigated the role of friction in compaction and segregation of dense granular packings. We incorporated friction into the thermodynamic hypothesis of Edwards, and analyzed grain segregation in this context. This provided a testable consequence of the Edwards approach.

Role of friction in compaction and segregation of granular materials

Y. Srebro and D. Levine**Physical Review E** 68, 061301 (2003)

Exactly solvable model for driven dissipative systems

Y. Srebro and D. Levine**Physical Review Letters** 93, 240601 (2004)

Comment on "Temperature in nonequilibrium systems with conserved energy"

Y. Srebro and D. Levine**Physical Review Letters** 94, 208901 (2005)

Fluctuation-dissipation relations in driven dissipative systems

Y. Shokef, G. Bunin, and D. Levine**Physical Review E** 73, 046132 (2006)

Energy distribution and effective temperatures in a driven dissipative model

Y. Shokef and D. Levine**Physical Review E** 74, 051111 (2006)

Isolated non-equilibrium systems in contact

Y. Shokef, G. Shulkind, and D. Levine**Physical Review E** 76, 030101(R) (2007)

Frequency-dependent fluctuation-dissipation relations in granular gases

G. Bunin, Y. Shokef, and D. Levine**Physical Review E** 77, 051301 (2008)