Emergent equilibrium-like yields from nonequilibrium cascade dynamics

TL;DR

This paper investigates nonequilibrium cascade processes that form fragile structures via intermediate states, revealing how memory effects influence dynamics and the validity of rate equations in complex systems.

Contribution

It introduces a framework connecting rate equations to Markovian approximations and highlights the role of non-Markovian memory effects in nonequilibrium cascade dynamics.

Findings

Rate equations emerge as Markovian approximations of complex dynamics.

Memory effects cause delayed and history-dependent formation processes.

Memory time quantifies the validity range of simplified rate descriptions.

Abstract

We study nonequilibrium cascades in which fragile bound or coherent structures are formed through intermediate states rather than by direct equilibration. Motivated by light-nuclei production in relativistic heavy-ion collisions and by Bose--Einstein condensation in cosmological settings, we analyze such processes within the Schwinger--Keldysh real-time formalism. We show that commonly used rate equations can be understood as a controlled Markovian approximation obtained by integrating out intermediate reservoirs in an underlying multi-component nonequilibrium dynamics. When the finite lifetime of these reservoirs is retained, non-Markovian memory effects naturally appear, leading to delayed and history-dependent formation dynamics. The associated memory time provides a quantitative criterion for the validity of reduced, rate-based descriptions far from equilibrium.