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.
Highlights
Entropy is considered as a measurement of randomness of thermodynamic systems [1,2,3,4]
The HJIconstrained optimization problems for solving the system entropy and energy dissipativity of nonlinear biological system could be replaced by the corresponding linear matrix inequality (LMI)-constrained optimization problems, which could be efficiently solved with help of LMI toolbox in Matlab [23, 43,44,45]
In the nonlinear biological systems, based on the global linearization technique, we could find that the same relationship between system entropy and energy dissipativity is maintained at the phenotype near the equilibrium point xe
Summary
Entropy is considered as a measurement of randomness of thermodynamic systems [1,2,3,4]. The global linearization method is introduced to interpolate several linearized local biological systems to approximate the nonlinear biological system [23, 42] In this way, the nonlinear HJI could be interpolated by a set of LMIs. In this way, the nonlinear HJI could be interpolated by a set of LMIs In this situation, the HJIconstrained optimization problems for solving the system entropy and energy dissipativity of nonlinear biological system could be replaced by the corresponding LMI-constrained optimization problems, which could be efficiently solved with help of LMI toolbox in Matlab [23, 43,44,45]. Two in silico examples of a phosphorelay biological system and a predatorprey ecological system are given to illustrate how to measure the system entropy and energy dissipativity and to confirm their relationship investigated by the proposed method
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
