Entropy and Stability in Blockchain Consensus Dynamics

Every Blockchain architecture is built upon two major pillars: a. The hash-based, block-binding mechanism and b. The consensus-achievement mechanism. While the entropic behavior of a. has been extensively studied in the literature over the past decades, the same does not hold for b. In this work, we explore the entropic behavior of the fully distributed Blockchain consensus mechanisms. We quantify the impact of witnessing as a consensus-achievement process under the perspectives of Shannon information entropy and Lyapunov stability. We demonstrate that Blockchain consensus, expressed as the complement of the collective disagreement in a system, is a Lyapunov function of the number of active witnesses W. The more the witnessing in a system, the less the entropy of the system becomes, pushing it to converge to more stable states. We prove that the entropy drop is steepest for low values of W. A new metric for the efficiency of the consensus process based on the Shannon information entropy is introduced, laying the foundations for future studies on Blockchain-based systems optimization.