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DY: Fachverband Dynamik und Statistische Physik

DY 55: Poster: Noneq. Stat. Phys., Stat. Bio. Phys., Brownian

DY 55.5: Poster

Donnerstag, 4. April 2019, 15:00–18:00, Poster B2

Characterizing non-equilibrium steady states via invariant manifolds — •Prakhar Godara, Jens Lucht, Marco Mazza, and Stephan Herminghaus — MPI für Dynamik und Selbstorganisation, Göttingen

It is still an unsolved question whether there is a general way to predict the steady state of a driven (non-equilibrium) system (a convection roll, a spiral wave, spatiotemporal chaos etc.) solely from its microscopic physics. The main obstacle is that detailed balance is breached in such systems. However, by describing the system not in state space, but instead in the space of all possible closed cycles in that space, detailed balance reappears. We demonstrate for the two-dimensional Fokker-Planck equation that the transition rates in this `cycle space' can be obtained from simple integrals of the drift field and the diffusion field, yielding a general potential in cycle space. The occupation probabilities of the non-equilibrium steady states, which correspond to the invariant manifolds of the drift field, are then given by a Boltzmann factor containing this potential. We corroborate our findings numerically.