Equivalence principle and critical behaviour for nonequilibrium decay modes

TL;DR

This paper extends the concept of orthonormality of decay modes from equilibrium to nonequilibrium Markovian systems, linking spectral properties to phase transitions and critical behavior.

Contribution

It introduces a generalized orthonormality relation for nonequilibrium decay modes and relates it to a statistical equivalence principle involving the Fisher-Rao metric.

Findings

Degenerate Fisher matrix indicates phase transitions in nonequilibrium systems.

Identifies an order parameter with power-law critical decay.

Proves divergent correlations between unbiased estimators near criticality.

Abstract

We generalize an orthonormality relation between decay eigenmodes of equilibrium systems to nonequilibrium markovian generators which commute with their time-reversal. Viewing such modes as tangent vectors to the manifold of statistical ensembles, we relate the result to the choice of a coordinate patch which makes the Fisher-Rao metric euclidean at the invariant state, realizing a sort of statistical equivalence principle. Finally, we classify nonequilibrium systems according to their spectrum, arguing that a degenerate Fisher matrix is a signature of the insurgence of a class of phase transitions between nonequilibrium regimes. We exhibit an order parameter with power-law critical decay and prove divergent correlations between suitable unbiased estimators.