Mathematical Physics Seminar (Nov 23rd) – Dr Jeremy O’Byrne – Non-Equilibrium Stochastic Field Theories: a Geometric Insight
Abstract: Probability currents are crucial features of statistical irreversibility. In steady-state, these currents are divergence-free and hence display a typically swirling behaviour. For a Langevin equation in 3D, this behaviour is well described by the curl of the mean velocity field — a.k.a. “vorticity” or “cycle affinity”. In higher but finite dimension, the curl is replaced by its generalization: the exterior derivative.
We introduce a functional version of the exterior derivative and show that the corresponding functional vorticity (or cycle affinity) provides valuable insight into out-of-equilibrium field theories, from the shape of their stationary probability currents to the counterparts of these currents in the physical space. For instance, in the case of the active model B — that is a minimal field theoretic description of the so-called motility induced phase separation — the latter correspond to the permanent excitation of anisotropic, propagating modes that are localized at the gas-liquid interface.
Furthermore, for stochastic vector fields over a one-dimensional space, we exhibit a basis of functional cycle affinities. The elements of this basis can be seen as independent sources of irreversibility on which the entropy production rate can be decomposed. In addition, these basis elements allow classifying the potential out-of-equilibrium behaviours the field theory can display.
Note: this seminar will be happening in-person.
Location: Huxley 342 + zoom meeting for those who can not attend in person
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