Abstract
We investigate the geometric structure of a nonequilibrium process and its geodesic solutions. By employing an exactly solvable model of a driven dissipative system (generalized nonautonomous OrnsteinUhlenbeck process), we compute the timedependent probability density functions (PDFs) and investigate the evolution of this system in a statistical metric space where the distance between two points (the socalled information length) quantifies the change in information along a trajectory of the PDFs. In this metric space, we find a geodesic for which the information propagates at constant speed, and demonstrate its utility as an optimal path to reduce the total time and total dissipated energy. In particular, through examples of physical realizations of such geodesic solutions satisfying boundary conditions, we present a resonance phenomenon in the geodesic solution and the discretization into cyclic geodesic solutions. Implications for controlling population growth are further discussed in a stochastic logistic model, where a periodic modulation of the diffusion coefficient and the deterministic force by a small amount is shown to have a significant controlling effect.
Original language  English 

Article number  062127 
Journal  Physical Review E 
Volume  93 
Issue number  6 
DOIs  
Publication status  Published  20 Jun 2016 
Externally published  Yes 
ASJC Scopus subject areas
 Statistical and Nonlinear Physics
 Statistics and Probability
 Condensed Matter Physics
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Eunjin Kim
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