The free energy requirements of biological organisms; implications for evolution

Recent advances in nonequilibrium statistical physics have provided unprecedented insight into the thermodynamics of dynamic processes. The author recently used these advances to extend Landauer's semi-formal reasoning concerning the thermodynamics of bit erasure, to derive the minimal free energy required to implement an arbitrary computation. Here, I extend this analysis, deriving the minimal free energy required by an organism to run a given (stochastic) map $\pi$ from its sensor inputs to its actuator outputs. I use this result to calculate the input-output map $\pi$ of an organism that optimally trades off the free energy needed to run $\pi$ with the phenotypic fitness that results from implementing $\pi$. I end with a general discussion of the limits imposed on the rate of the terrestrial biosphere's information processing by the flux of sunlight on the Earth.Comment: 19 pages, 0 figures, presented at 2015 NIMBIoS workshop on "Information and entropy in biological systems

Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principled formulation of bounded rationality and a set of new types of mean field theory in statistical physics. It also shows that those topics are fundamentally one and the same.Comment: 17 pages, no figures, accepted for publicatio

An adaptive Metropolis-Hastings scheme: sampling and optimization

We propose an adaptive Metropolis-Hastings algorithm in which sampled data are used to update the proposal distribution. We use the samples found by the algorithm at a particular step to form the information-theoretically optimal mean-field approximation to the target distribution, and update the proposal distribution to be that approximatio. We employ our algorithm to sample the energy distribution for several spin-glasses and we demonstrate the superiority of our algorithm to the conventional MH algorithm in sampling and in annealing optimization.Comment: To appear in Europhysics Letter

Distributed Control by Lagrangian Steepest Descent

Often adaptive, distributed control can be viewed as an iterated game between independent players. The coupling between the players' mixed strategies, arising as the system evolves from one instant to the next, is determined by the system designer. Information theory tells us that the most likely joint strategy of the players, given a value of the expectation of the overall control objective function, is the minimizer of a Lagrangian function of the joint strategy. So the goal of the system designer is to speed evolution of the joint strategy to that Lagrangian minimizing point, lower the expectated value of the control objective function, and repeat. Here we elaborate the theory of algorithms that do this using local descent procedures, and that thereby achieve efficient, adaptive, distributed control.Comment: 8 page