Monday 07 Dec 2015Statistical distance and geodesics in non-equilibrium systems (GAFD Seminar)

Dr Eun-Jin Kim - The University of Sheffield

Harrison 103 14:30-16:00

Many systems in nature are nonlinear and involve stochastic processes due to intrinsic variability, heterogeneity, or uncertainty in a system. In understanding the time-evolution of a system far from equilibrium, one of the main challenges is the computation of the probability density function (PDF), in particular, its time-evolution.

In this talk, we discuss how to measure the distance between different states in non-equilibrium systems and present a study on the geometric structure of a strongly out of equilibrium system using an exactly solvable model [1]. In particular, by utilising a dynamical ruler whose resolution is set by time-dependent fluctuations associated with information change, we map the evolution of a non-equilibrium system into a trajectory in a generalised statistical metric space, where the distance between two points along the trajectory quantifies the change in information (e.g. [2]), which reveals the structure of the attractor. We then present a geodesic for which the information propagates at the constant speed and discuss it implications for controlling a system by an optimal "treatment" protocol.

[1] U. Lee, J.J. Skinner, J. Reinitz, M.R. Rosner, and E. Kim, PLoS One, 10, e0132397 (2015).

[2] S.B. Nicholson and E. Kim, Phys. Lett. A., 379, 8388 (2015).

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