Thermodynamics and evolutionary biology through optimal control

Abstract

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. * alessandro.bravetti@cimat.mx †

Features of the Bone System Formation of Carcasses of Simmental and Crossbreed Steers

“…In biology, to analyze and describe the growth, development, and aging of organisms, the evolutionary criterion of thermodynamics of linear irreversible processes, based on the theory of I. Prigogine and J. M. Wiame (Bravetti and Padilla, 2019), the essence of which is that in the stationary state of an organism, the production of entropy (useless energy dissipating in space) is minimal and constant within an open thermodynamic system when external parameters are constant. If a living system deviates from its stationary state under the influence of various factors, it will tend to be constant until the entropy production is again minimal.…”

Contact variational integrators

“…Contact geometry appears in fluid dynamics [19,38,47], thermodynamics [7,28,29,43,53], statistical physics [9], statistics [5,27], quantum mechanics [11,14,21,33,46], gravity [40], information geometry [3,4,26], shape dynamics [52], biology [8,30], optimal control [37,45], and integrable systems [6,35,36,49,50]. One of the applications that has recently attracted a lot of attention is the classical mechanics of dissipative systems [1,2,10,17,18,23,41], on which we will focus in this paper.…”