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Related Concept Videos

Entropy02:39

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
Entropy01:18

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
Absolute Entropies and the Third Law of Thermodynamics01:23

Absolute Entropies and the Third Law of Thermodynamics

Ludwig Edward Boltzmann developed a definition for entropy, which stated that absolute entropy is proportional to the natural logarithm of the number of possible combinations of particles. Entropy stands alone among state functions as the only one whose absolute values can be determined.Consider a gas sample confined to a container. As the container expands, the energy levels of gas molecules become more closely spaced. This increases the number of available energy states, thereby increasing...
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
Entropy and the Second Law of Thermodynamics01:26

Entropy and the Second Law of Thermodynamics

Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...

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Related Experiment Videos

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

Lanlan Li1,2, Charles Z Liu2,3, Sanjeeb Shrestha4

  • 1School of Information Engineering, Chuzhou Polytechnic, Chuzhou 239000, China.

Entropy (Basel, Switzerland)
|June 26, 2026
PubMed
Summary

Entropy metrics offer a novel way to assess blockchain security. This study shows entropy quantifies ledger immutability and detects tampering, enhancing distributed ledger technology resilience.

Keywords:
attack resilienceblockchainblockchain virtual machineconsensus mechanismentropyimmutabilityinformation theoryoff-chain data securityon-chain data integritysmart contracts

Related Experiment Videos

Area of Science:

  • Computer Science
  • Information Theory
  • Cryptography

Background:

  • Blockchain systems rely on consensus mechanisms for security and immutability.
  • Current methods for evaluating blockchain security lack robust, quantitative metrics.
  • Understanding computational dynamics within blockchain virtual machines is crucial for protocol design.

Purpose of the Study:

  • To develop and apply entropy-based metrics for evaluating blockchain systems.
  • To quantify on-chain ledger immutability, off-chain data integrity, and computational dynamics.
  • To provide a unified framework for assessing blockchain security under adversarial conditions.

Main Methods:

  • Modeling blockchain states as probabilistic distributions.
  • Quantifying uncertainty using Shannon entropy.
  • Analyzing entropy evolution under varying adversarial fractions through simulations.
  • Examining computation entropy within blockchain virtual machines (BVMs).

Main Results:

  • On-chain entropy shows near-exponential decay, indicating reinforced honest consensus.
  • Off-chain entropy remains static, revealing limitations in conventional data storage.
  • BVM computation entropy confirms Turing completeness and mirrors Turing machine information dynamics.

Conclusions:

  • Entropy serves as a theoretical and operational measure of blockchain immutability, tamper evidence, and protocol resilience.
  • The proposed entropy framework provides practical tools for monitoring ledger integrity and detecting tampering.
  • This study advances the understanding and evaluation of blockchain security using information-theoretic principles.