Universality in Driven and Equilibrium Hard Sphere Liquid Dynamics

Why Noether's Theorem applies to Statistical Mechanics

“…The dynamical sum rules for forces and correlation functions presented in Ref. [14] offer great potential for systematic progress in complex time behaviour, including memory [41,42]. Together with the nonequilibrium Ornstein-Zernike relations [39,40] they provide a fertile ground for making progress in nonequilibrium physics.…”

“…In Ref. [14] we also apply Noether's thinking to a very recent variational approach for dynamics, called power functional theory [28], which propels the functional concepts from equilibrium to nonequilibrium [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42], including the recently popular active Browian particles [43][44][45][46][47][48][49]. The generalization is important, as it shows that not only a dead Munchausen cannot bootstrap himself out of his misery, but that being alive does not help (in this particular case).…”

Dynamic Decay and Superadiabatic Forces in the van Hove Dynamics of Bulk Hard Sphere Fluids

“…Data is shown from BD simulation (green long dashes) and from DDFT with the full (yellow long dot-dashes), quenched (red medium dot-dashes) and partially linearised (purple short dot-dashes) excess free energy functional. Additionally, we show the long-time self diffusion (black short dashes) as calculated from our PFT approximation (57). As a reference, the linear law of ideal diffusion (blue solid line) is also plotted.…”

“…This work builds upon an approximation developed for viscolelastic forces in a sheared system of hard spheres [58] and approximations developed for drag-like and structural forces in a binary system of counterdriven hard spheres [59]. In [57], we have shown that superadiabatic forces contribute significantly to the internal force field at all times. Our approximation describes the internal force field accurately starting at short times t > 0.3τ up to at least t = 1.5τ, where τ ≡ σ 2 /D is the intrinsic Brownian timescale of the system, with particle diameter σ and diffusion constant D.…”

“…Despite these successes, studies of the van Hove function with DDFT systematically neglect superadiabatic effects by construction [46,47]. Recently, we have combined viscoelastic, draglike and structural forces to obtain an approximation for superadiabatic forces in the dynamics of the hard sphere van Hove function [57]. This work builds upon an approximation developed for viscolelastic forces in a sheared system of hard spheres [58] and approximations developed for drag-like and structural forces in a binary system of counterdriven hard spheres [59].…”