Absorbing phase transitions with memory in critical scaling

TL;DR

This paper reveals that in certain driven systems with absorbing states, the long-term behavior can depend on initial conditions due to the configuration space fracturing into multiple classes, challenging the universality of critical scaling.

Contribution

It demonstrates that memory effects in absorbing phase transitions can lead to nonuniqueness of quasi-stationary states, contrary to previous assumptions of universality.

Findings

Memory effects influence critical exponents near absorbing transitions.

Quasi-stationary states become nonunique when birth processes are suppressed.

Configuration space fragmentation causes initial-condition dependence.

Abstract

Many driven systems alternate between bursts of activity and quiescence and can become trapped in an absorbing state, such as complete inactivity in reaction-diffusion processes or extinction in predator-prey dynamics. It is generally assumed that, conditioned on survival, their long-lived (quasi-stationary) behavior is unique and independent of the initial condition. We show this need not hold, even for memoryless Markov dynamics. When the configuration space fractures into multiple macroscopic communicating classes, where configurations can be reach from one another within a class but not across classes, the system retains a measurable memory of its preparation, which can directly affect the critical exponents near absorbing transitions. Using a minimal birth-death-diffusion model, we demonstrate that the quasi-stationary state is unique when birth processes are present, but becomes nonunique and initial-condition dependent when they are suppressed. This mechanism, arising from vanishing of inter-class escape-rate ratios in thermodynamic limit, challenges the conventional universality hypothesis and suggests possibility of history-dependent critical scaling in controlled lattice or colloidal systems with tunable particle-number.