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We consider discrete stochastic processes, modeled by classical masterequations, on networks. The temporal growth of the lack of information aboutthe system is captured by its non-equilibrium entropy, defined via thetransition probabilities between different nodes of the network. We derive arelation between the entropy and the spectrum of the master equation's transfermatrix. Our findings indicate that the temporal growth of the entropy isproportional to the logarithm of time if the spectral density shows scaling. Inanalogy to chaos theory, the proportionality factor is called (stochastic)information dimension and gives a global characterization of the dynamics onthe network. These general results are corroborated by examples of regular andof fractal networks.

Information Dimension of Stochastic Processes on Networks: Relating Entropy Production to Spectral Properties