The Thermodynamics of Network Coding, and an Algorithmic Refinement of the Principle of Maximum Entropy

The principle of maximum entropy (Maxent) is often used to obtain prior probability distributions as a method to obtain a Gibbs measure under some restriction giving the probability that a system will be in a certain state compared to the rest of the elements in the distribution. Because classical entropy-based Maxent collapses cases confounding all distinct degrees of randomness and pseudo-randomness, here we take into consideration the generative mechanism of the systems considered in the ensemble to separate objects that may comply with the principle under some restriction and whose entropy is maximal but may be generated recursively from those that are actually algorithmically random offering a refinement to classical Maxent. We take advantage of a causal algorithmic calculus to derive a thermodynamic-like result based on how difficult it is to reprogram a computer code. Using the distinction between computable and algorithmic randomness we quantify the cost in information loss associated with reprogramming. To illustrate this we apply the algorithmic refinement to Maxent on graphs and introduce a Maximal Algorithmic Randomness Preferential Attachment (MARPA) Algorithm, a generalisation over previous approaches. We discuss practical implications of evaluation of network randomness. Our analysis provides insight in that the reprogrammability asymmetry appears to originate from a non-monotonic relationship to algorithmic probability. Our analysis motivates further analysis of the origin and consequences of the aforementioned asymmetries, reprogrammability, and computation.Comment: 30 page

Emergence and algorithmic information dynamics of systems and observers

Previous work has shown that perturbation analysis in software space can produce candidate computable generative models and uncover possible causal properties from the finite description of an object or system quantifying the algorithmic contribution of each of its elements relative to the whole. One of the challenges for defining emergence is that one observer's prior knowledge may cause a phenomenon to present itself to such observer as emergent while for another as reducible. When attempting to quantify emergence, we demonstrate that the methods of Algorithmic Information Dynamics can deal with the richness of such observer-object dependencies both in theory and practice. By formalising the act of observing as mutual algorithmic perturbation, the emergence of algorithmic information is rendered invariant, minimal, and robust in the face of information cost and distortion, while still observer-dependent. We demonstrate that the unbounded increase of emergent algorithmic information implies asymptotically observer-independent emergence, which eventually overcomes any formal theory that an observer might devise to finitely characterise a phenomenon. We discuss observer-dependent emergence and asymptotically observer-independent emergence solving some previous suggestions indicating a hard distinction between strong and weak emergence