Thermodynamics and evolutionary biology through optimal control

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.