Analytical Entropy Approach for Measuring Blockchain Immutability and Tamper-Resilient Trust

This work presents a comprehensive study of entropy-based metrics for evaluating blockchain systems, focusing on on-chain ledger immutability, off-chain data integrity, and computational dynamics within blockchain virtual machines (BVMs). We develop a unified framework that models blockchain states as probabilistic distributions, quantifying uncertainty through Shannon entropy and examining its evolution under varying adversarial fractions. Extensive simulations demonstrate that on-chain entropy exhibits near-exponential decay, reflecting the cumulative reinforcement of honest consensus, while off-chain entropy remains static, highlighting the limitations of conventional data storage. Furthermore, the BVM is analyzed in terms of computation entropy, establishing its Turing completeness and demonstrating that smart-contract state evolution mirrors the information dynamics of arbitrary Turing machines. Our results provide quantitative evidence that entropy serves as both a theoretical and operational measure of immutability, tamper evidence, and protocol resilience. The proposed entropy framework offers practical tools for monitoring ledger integrity, detecting tampering, and assessing computational complexity, bridging the gap between information-theoretic principles and distributed ledger applications. This study advances both the theoretical understanding and practical evaluation of blockchain security, providing a principled methodology for analyzing distributed systems under adversarial conditions.