Image of the Week: Markov jumps and current fluctuations

By Phil Brown on July 3, 2017

This week’s image is taken from a study Inferring dissipation from current fluctuations as part of the Emerging Talents special issue on Journal of Physics A. Todd R Gingrich, Grant M Rotskoff and Jordan M Horowitz study Markov jumps in mesoscopic systems. They study the impact of spatial coarse-graining in a two-dimensional model with driven diffusion. And by observing fluctuations in the coarse-grained currents, they can infer a lower bound on the total dissipation rate, including the dissipation associated with hidden dynamics.

$A jump process approximates the diffusion in figure 4. On the left, a close-up view of a sub-system shows the transition rates on the lattice. On the right, the steady-state behavior of the full state space $(\boldsymbol{x} \in [-2, 2] \times [-2, 2])$ is shown for $A = 8, B = 5, D = 1, \mu = 1$ . The steady-state density primarily resides in the four wells, but the external field drives some clockwise current around the origin.$

A jump process approximates diffusion. On the left, a close-up view of a sub-system shows the transition rates on the lattice. On the right, the steady-state behavior of the full state space. The steady-state density primarily resides in the four wells, but the external field drives some clockwise current around the origin. From Todd R Gingrich et al 2017 J. Phys. A: Math. Theor. 50 184004 Copyright IOP Publishing.

The image describes a diffusion process. The image itself comprises two panels. The left hand panel shows the Markov jump processes and the right hand panel shows the steady-state density. The steady-state density can be seen to collect around four wells, but with a small clockwise flowing current shown by the orange arrows in the diagram. The source of the clockwise flowing current is an external field.

Todd Gingrich is a Physics of Living Systems Fellow at MIT and was selected as an Emerging Talent by the JPhysA board. Todd is excited to be joining Northwestern University’s Department of Chemistry in Autumn 2018 as an Assistant Professor.

Special Issue: Emerging Talents

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