Dynamic transition in a Brownian fluid: role of fluctuation–dissipation constraints

In this paper we study equations of fluctuating non-linear hydrodynamics (FNH) for a liquid in which the constituent particles follow Brownian dynamics (BD). Here the microscopic-level dynamics are dissipative as compared to the case of fluids with reversible Newtonian dynamics (ND). The implications of non-linearities in FNH equations for an ND liquid on its long-time dynamics and the possibility of an ideal ergodicity–non-ergodicity (ENE) transition at high density have been widely investigated in literature. It is known that in an ND fluid, dynamics described by FNH equations do not support a sharp ENE transition. In the present paper we demonstrate that, as a consequence of the fluctuation–dissipation constraints, an ideal ENE transition is also not supported from the FNH equations for BD fluid. (paper: classical statistical mechanics, equilibrium and non-equilibrium)