  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.
