The role of dimensionality and geometry in quench-induced nonequilibrium forces

TL;DR

This paper develops an analytical and numerical framework to study the time-dependent forces on curved boundaries after temperature quenches in Brownian fluids, revealing dimension-dependent algebraic decay and boundary-specific force behaviors.

Contribution

It introduces a formalism for analyzing nonequilibrium forces on curved geometries post-quench, highlighting the impact of curvature and system dimension on force evolution.

Findings

Forces rapidly reach an extremum after a quench.

Steady-state forces decay as t^{-d/2} in d-dimensional spherical geometries.

Inner boundary forces exhibit overshoot and complex evolution.

Abstract

We present an analytical formalism, supported by numerical simulations, for studying forces that act on curved walls following temperature quenches of the surrounding ideal Brownian fluid. We show that, for curved surfaces, the post-quench forces initially evolve rapidly to an extremal value, whereafter they approach their steady state value algebraically in time. In contrast to the previously-studied case of flat boundaries (lines or planes), the algebraic decay for the curved geometries depends on the dimension of the system. Specifically, the steady-state values of the force are approached in time as $t^{-d/2}$ in d-dimensional spherical (curved) geometries. For systems consisting of concentric circles or spheres, the exponent does not change for the force on the outer circle or sphere. However, the force exerted on the inner circle or sphere experiences an overshoot and, as a result, does not evolve towards the steady state in a simple algebraic manner. The extremal value of the force also depends on the dimension of the system, and originates from the curved boundaries and the fact that particles inside a sphere or circle are locally more confined, and diffuse less freely than particles outside the circle or sphere.