Entropy and Stability in Blockchain Consensus Dynamics
Every Blockchain architecture relies 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 literature over the past decades, the same does not hold for (b). In this work, we...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-02-01
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| Series: | Information |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2078-2489/16/2/138 |
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| Summary: | Every Blockchain architecture relies 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 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 <i>witnessing</i> as a <i>consensus-achievement process</i> under the perspectives of <i>Shannon information entropy</i> and <i>Lyapunov stability</i>. We demonstrate that Blockchain consensus, expressed as the <i>complement of the collective disagreement</i> in a system, is a <i>Lyapunov function</i> of the number of <i>witnesses W</i>. The more the <i>witnessing</i> in a system, the less the <i>entropy</i> of the system becomes, and it converges to <i>more stable states</i>. We prove that the <i>entropy decline</i> is <i>steepest</i> for low values of <i>W</i>. A new metric for the efficiency of the <i>consensus process</i> based on the <i>Shannon information entropy</i> is introduced, laying the foundations for future studies on Blockchain-based systems optimization. |
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| ISSN: | 2078-2489 |