Emergent equilibrium-like yields from nonequilibrium cascade dynamics

TL;DR

The paper addresses how equilibrium-like yields can emerge from nonequilibrium cascades that proceed through intermediate reservoirs. Using the Schwinger--Keldysh real-time formalism, it shows that conventional rate equations are the Markovian limit obtained after integrating out an intermediate reservoir, with memory effects encoded by the reservoir lifetime. A central result is that the validity of rate-based descriptions is controlled by the memory time: short reservoir lifetimes recover local rates, while longer lifetimes generate non-Markovian, delayed formation dynamics observable in quantities like the coalescence parameter $B_2$. By linking heavy-ion collision dynamics mediated by the $\Delta$ resonance to cosmological Bose--Einstein condensation, the work reveals a universal nonequilibrium structure where intermediate reservoirs govern the transfer of correlations and the emergence of quasi-equilibrium yields, offering a principled framework to assess rate-model applicability and predict memory-induced signatures.

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.