Nonequilibrium identities and response theory for dissipative particles

Abstract

We derive some nonequilibrium identities such as the integral fluctuation theorem and the Jarzynski equality starting from a nonequilibrium state for dissipative classical systems. Thanks to the existence of the integral fluctuation theorem we can naturally introduce an entropy-like quantity for dissipative classical systems in far from equilibrium states. We also derive the generalized GreenKubo formula as a nonlinear response theory for a steady dynamics around a nonequilibrium state. We numerically verify the validity of the derived formulas for sheared frictionless granular particles.

Effect of elastic vibrations on normal head-on collisions of isothermal spheres

“…In the super rebounds, parts of elastic vibrations are transferred to translational motion of the colliding bodies and thus kinetic energy of the translational motion of it can increase after the collision. The super rebound is associated with the decreases of entropy [34] and the fluctuation theorem [47][48][49][50][51][52][53][54]. Indeed, Tasaki indicated that the probability of the restitution coefficient can satisfy an extended fluctuation theorem if the motion of the center of mass can be separated from the motion of internal degrees of freedoms [55].…”

Nonequilibrium identities of granular vibrating beds

“…For example, Ref. [24] uses 18 grains with 800,000 samples. It should be noted that the verification of the generalized Green-Kubo formula is not difficult by the direct simulation, but the confirmation of the integral fluctuation theorem by simulations is not easy because of the limitation of numerical accuracy.…”

“…They also developed the representation of a nonequilibrium steady-state distribution function [22] and the liquid theory for sheared dense granular systems [23]. Recently, Hayakawa and Otsuki [24] extended their previous formulation to discuss nonequilibrium identities around a nonequilibrium steady state, and also demonstrate their validity from the direct comparison between the obtained identities and the numerical simulations.…”

A microscopic theory for discontinuous shear thickening of frictional granular materials

“…where Ω ≡ βḢ − Λ = −γβS σ xy − 2βR + βJ − Λ with the inverse of granular temperature, β ≡ 1/ T γ , is the work function [6,9] and σ xy γ 0. Assuming an exponential decay of the time correlation function, σ xy (s)Ω γ ≃ σ xy Ω γ e −s/τ rel , with a relaxation time, τ rel , and taking a long time limit (t → ∞), we reduce Eq.…”