Colored Cross-Correlated Noises Driven Dynamical Systems: Time Dependence of Information Entropy and Its Time Derivative

Abstract

In this paper we have studied information entropy and its time derivative for colored cross-correlated noise driven open systems. These quantities are calculated based on the Fokker-Planck description of stochastic processes. Our results consider the effect of the noise correlation strength and correlation time due to the correlation between additive and multiplicative white noises on the information entropy as well as relaxation time. The interplay of deterministic and random forces reveals non-monotonic behavior in the variation of the information entropy with damping constant.Study of noise driven dynamical system is always an intriguing issue in physics since random processes are ubiquitous in almost all disciplines of natural sciences such as physics, chemistry, biology [1-6]. An appropriate tool for the study of stationary and non-stationary states [7][8][9][10][11][12][13][14][15][16] in stochastic processes is Shanon's information measure [17,18] which typically is not a conserved quantity. Here W (q, t) is the continuous probability distribution. S as defined in the above equation is called information entropy. The time derivative of information entropy (dS/dt) is related to another very important quantity, Fisher's information measure [19]. Recent studies [7][8][9][10][11][12][19][20][21] show that these quantities are vital to the study of the stochastic process in detail. The dS/dt has been studied in the context of Brownian motion in the presence of temperature gradient and thermodynamics beyond local equilibrium in Refs. [22,23]. It has been also studied even in the social science (the majority-vote model) [15]. There [15] authors showed that the time derivative of information entropy exhibits a singularity at the critical point. In Ref.[16] authors has been studied