Reprogramming a generative mechanism to produce a different object is associated with a cost. Here we use the notion of algorithmic randomness to quantify such a cost when reprogramming networks. We identify an asymmetry in a measure of reprogrammability,
suggesting an analogy with a thermodynamic asymmetry. The principle of maximum entropy (Maxent) quantifies the evolution of entropy or the uncertainty during state transitions in systems confined to an equilibrium condition. Here we define a generalisation
based on algorithmic randomness not restricted to equilibrium physics, based on both distance to algorithmic randomness and reprogrammability. We advance a constructive preferential attachment algorithm approximating a maximally algorithmic random
Hence, as a refinement on classical Maxent, networks can be quantified with respect to their distance to a maximally algorithmic random network. Our analysis suggests that the reprogrammability asymmetry originates from its non-monotonic relationship to algorithmic randomness. Our analysis motivates further work on the degree of algorithmic asymmetries in systems depending on their reprogrammability capabilities.
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