2,726 research outputs found
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 from its sensor inputs to its actuator outputs. I use
this result to calculate the input-output map of an organism that
optimally trades off the free energy needed to run with the phenotypic
fitness that results from implementing . 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
Metrics for more than two points at once
The conventional definition of a topological metric over a space specifies
properties that must be obeyed by any measure of "how separated" two points in
that space are. Here it is shown how to extend that definition, and in
particular the triangle inequality, to concern arbitrary numbers of points.
Such a measure of how separated the points within a collection are can be
bootstrapped, to measure "how separated" from each other are two (or more)
collections. The measure presented here also allows fractional membership of an
element in a collection. This means it directly concerns measures of ``how
spread out" a probability distribution over a space is. When such a measure is
bootstrapped to compare two collections, it allows us to measure how separated
two probability distributions are, or more generally, how separated a
distribution of distributions is.Comment: 8 page
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
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