Thermodynamics and evolutionary biology through optimal control. (August 2019)

• Record Type: Journal Article
• Authors: Bravetti, Alessandro; Padilla, Pablo
• Is Part Of: Automatica. Volume 106(2019)
• Page Start: 201
• Page End: 206
• Publication Date: 2019-08
• Subjects: Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2019.05.017
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: We consider a particular instance of the lift of controlled systems proposed in the theory of irreversible thermodynamics and show that it is equivalent to a variational principle for an optimal control in the sense of Pontryagin. Then we focus on two important applications: in thermodynamics and in evolutionary biology. In the thermodynamic context, we show that this principle provides a dynamical implementation of the Second Law, which stabilizes the equilibrium states of a system. In the evolutionary context, we show that our principle leads directly to the Optimal Replicator Equation, and we discuss several interesting features: it provides a robust scheme for the coevolution of the population and its fitness landscape; it has a clear formulation in terms of an optimization process; and finally, it extends standard evolutionary dynamics to include phenomena such as the emergence of cooperation.