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Two principles explain emergence. First, in the Receipts reference frame, Deg(S) = 4/3 Deg(R), where Supply S is an isotropic radiative energy source, Receipt R receives Ss energy, and Deg is a systems degrees of freedom based on its mean path length. Ss 1/3 more degrees of freedom relative to R enables Rs growth and increasing complexity. Second, rho(R) = Deg(R) times rho(r), where rho(R) represents the collective rate of R and rho(r) represents the rate of an individual in R: as Deg(R) increases due to the first principle, the multiplier effect of networking in R increases. A universe like ours with isotropic energy distribution, in which both principles are operative, is therefore predisposed to exhibit emergence, and, for reasons shown, a ubiquitous role for the natural logarithm.
Transfer entropy has been used to quantify the directed flow of information between source and target variables in many complex systems. While transfer entropy was originally formulated in discrete time, in this paper we provide a framework for consi
We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find that these
We produce a series of results extending information-theoretical inequalities (discussed by Dembo--Cover--Thomas in 1989-1991) to a weighted version of entropy. The resulting inequalities involve the Gaussian weighted entropy; they imply a number of
What are the distinct ways in which a set of predictor variables can provide information about a target variable? When does a variable provide unique information, when do variables share redundant information, and when do variables combine synergisti
If each node of an idealized network has an equal capacity to efficiently exchange benefits, then the networks capacity to use energy is scaled by the average amount of energy required to connect any two of its nodes. The scaling factor equals textit