Equivalence principle and critical behaviour for nonequilibrium decay modes
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.
Cite
@article{arxiv.1105.4134,
title = {Equivalence principle and critical behaviour for nonequilibrium decay modes},
author = {Matteo Polettini},
journal= {arXiv preprint arXiv:1105.4134},
year = {2014}
}
Comments
This paper has been withdrawn by the author. New vastly revised version of this paper: Fisher information of Markovian decay modes - Nonequilibrium equivalence principle, dynamical phase transitions and coarse graining, arXiv:1409.4193