Thermodynamics and evolutionary biology through optimal control

We consider a particular instance of the lift of controlled systems recently proposed in the theory of irreversible thermodynamics and show that it leads 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 manifold of a system. In the evolutionary context, we discuss several interesting features: it provides a robust scheme for the coevolution of the population and its fitness landscape; it has a clear informational interpretation; it recovers Price equation naturally; and finally, it extends standard evolutionary dynamics to include phenomena such as the emergence of cooperation and the coexistence of qualitatively different phases of evolution, which we speculate can be associated with Darwinism and punctuated equilibria.