On the System Entropy and Energy Dissipativity of Stochastic Systems and Their Application in Biological Systems

Abstract

This study discusses the relationship between the entropy and the dissipativity of stochastic systems under the background of biological systems. First, measurement methods of the system entropy and energy dissipativity of linear stochastic biological systems are introduced. We found that the system entropy is negatively proportional to the energy dissipativity in logarithmic scale. Some opposite effects between system entropy and energy dissipativity are also discussed and compared based on their measured values to get insight into the understanding of the system mechanisms and the system characteristics. We found that the intrinsic random fluctuation and the enhancement of the system robust stability both can increase the system entropy but decrease the system dissipativity. The system entropy and the energy dissipativity of nonlinear stochastic biological systems are also discussed and compared based on a global linearization method. Computation methods are also provided. Finally, two numerical examples are demonstrated to verify theoretical prediction.