Dissipative signatures of dynamical phases and transitions

Daniel S. Seara, Benjamin B. Machta, Michael P. Murrell

Published 2019-11-25Version 1

Living and non-living active matter consumes energy at the microscopic scale to drive emergent, macroscopic behavior including traveling waves and coherent oscillations. Recent work has characterized non-equilibrium systems by their total energy dissipation, but little has been said about how dissipation manifests in distinct spatiotemporal patterns. We introduce a novel measure of dissipation we term the entropy production factor (EPF) to quantify how time reversal symmetry is broken in field theories across scales. We illustrate the use of this method on simulations of the Brusselator, a prototypical biochemically motivated non-linear oscillator. We find that while the total dissipation does not drastically change as the system undergoes a Hopf bifurcation, the EPF shows a dramatic change in the allocation of energy. The EPF measures how microscopic irreversibility propagates to larger length and time scales and integration through frequency space bounds the net dissipation of stochastic processes.