Upper bound of the time derivative of entropy for a dynamical system driven by two kinds of colored noise. (English) Zbl 1165.82315
Summary: The upper bound \(U_{B}(t)\) of the time derivative of entropy for a dynamical system driven by both additive colored noise and multiplicative colored noise with colored cross-correlation is investigated. Based on the Fokker–Planck equation, the effects of the parameters on \(U_{B}(t)\) are analyzed. The results show that: (i) \(\alpha\) (the multiplicative noise intensity), \(D\) (the additive noise intensity) and \(\tau_2\) (the correlation time of the additive noise) always enhance \(U_{B}(t)\) monotonically; (ii) \(\lambda\) (the intensity of the cross-correlation between the multiplicative noise and the additive noise), \(\tau_1\) (the correlation time of the multiplicative noise), \(\tau_3\) (the correlation time of the cross-correlation) and \(\gamma\) (the dissipative constant) all possess a minimum, i.e., \(U_{B}(t)\) decreases for small values and increases for large values.
MSC:
| 82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
| 94A17 | Measures of information, entropy |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
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