Ageing, dynamical scaling and its extensions in many-particle systems without detailed balance

TL;DR

This paper reviews recent findings on ageing phenomena in various many-particle systems at non-equilibrium critical points, highlighting differences from magnetic systems and examining scaling functions and fluctuation-dissipation ratios.

Contribution

It extends the understanding of ageing and dynamical scaling in non-equilibrium many-particle systems beyond traditional magnetic models, including systems without detailed balance.

Findings

Scaling relations between ageing exponents are not universally valid.

Universal limit fluctuation-dissipation ratio does not generalize straightforwardly.

Scaling function of the response aligns with local scale-invariance predictions.

Abstract

Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving branching-annihilating random walk, two exactly solvable particle-reaction models and kinetic growth models. While the generic scaling descriptions known from magnetic system can be taken over, some of the scaling relations between the ageing exponents are no longer valid. In particular, there is no obvious generalization of the universal limit fluctuation-dissipation ratio. The form of the scaling function of the two-time response function is compared with the prediction of the theory of local scale-invariance.