We have studied dynamics of both internal and external noises-driven dynamical system in terms of information entropy at both nonstationary and stationary states. Here a unified description of entropy flux and entropy production is considered. Based on the Fokker-Planck description of stochastic processes and the entropy balance equation we have calculated time dependence of the information entropy production and entropy flux in presence and absence of nonequilibrium constraint (NEC). In the presence of NEC we have observed extremum behavior in the variation of entropy production as function of damping strength, noise correlation, and non-Gaussian parameter (which determine the deviation of external noise behavior from Gaussian characteristic), respectively. Thus the properties of noise process are important for entropy production. 1. Introduction In recent years the stochastic dynamics [1–5] community is becoming increasingly interested to study the role of noise in dissipative dynamical systems, because of its potential applications on various noise-induced phenomena, such as noise-induced phase transition [6], noise-sustained structures in convective instability [7], stochastic spatiotemporal intermittency [8], noise-modified bifurcation [9], noise-induced traveling waves [10], noise-induced ordering transition [11], noise-induced front propagation [12], stochastic resonance [13–15], coherence resonance [16–19], synchronization [20, 21], clustering [22], noise-induced pattern formation [23, 24]. In the traditional classical thermodynamics, the specific nature of the stochastic process is irrelevant but it may play an important role on the way to equilibration of a given nonequilibrium state of the noise-driven dynamical system. The relaxation behavior of the stochastic processes can be understood using information entropy ( ). Now the information entropy becomes a focal theme in the field of stochastic processes [25–28]. In [27] the authors have been studied the transition from the slow-wave sleep to the rapid-eye-movement sleep in terms of the information entropy. Crochik and Tomé [28] calculated the entropy production in the majority-vote model and showed that the entropy production exhibits a singularity at the critical point. The time evolution of mainly considers the signature of the rate of phase space expansion and contraction in the random force-driven Brownian motion. This implies that the specific nature of the random process has a strong role to play with . In view of the importance of the characteristics of the frictional and the random
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