Monday 07 Dec 2015: Statistical 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 . 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. ), 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.
 U. Lee, J.J. Skinner, J. Reinitz, M.R. Rosner, and E. Kim, PLoS One, 10, e0132397 (2015).
 S.B. Nicholson and E. Kim, Phys. Lett. A., 379, 8388 (2015).