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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...
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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
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Multi-Additivity in Kaniadakis Entropy.

Antonio M Scarfone1, Tatsuaki Wada2

  • 1Istituto dei Sistemi Complessi-Consiglio Nazionale delle Ricerche (ISC-CNR), c/o Dipartimento di Scienza Applicata e Tecnologia del Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.

Entropy (Basel, Switzerland)
|January 22, 2024
PubMed
Summary
This summary is machine-generated.

Kaniadakis entropy, a generalized form of entropy, is shown to be multi-additive under specific constraints. This finding applies to classes of maximal entropy distributions composed of independent and identically distributed systems.

Keywords:
power-law distributionspseudo-additivityκ-entropy

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Area of Science:

  • Statistical Mechanics
  • Information Theory
  • Mathematical Physics

Background:

  • Kaniadakis entropy is a generalization of Shannon-Boltzmann-Gibbs entropy.
  • Kaniadakis entropy is known to be super-additive for bipartite statistically independent distributions.
  • Understanding entropic properties is crucial in various scientific domains.

Purpose of the Study:

  • To investigate the conditions under which Kaniadakis entropy exhibits multi-additivity.
  • To identify classes of maximal entropy distributions with this property.
  • To explore the implications for systems composed of independent and identically distributed distributions.

Main Methods:

  • Imposing a suitable constraint on distributions.
  • Analyzing the composition of two statistically independent and identically distributed distributions.
  • Deriving the multi-additive property Sκ[pA∪B]=(1+ℵ)Sκ[pA]+Sκ[pB] for Kaniadakis entropy.

Main Results:

  • Existence of maximal entropy distribution classes labeled by ℵ > 0.
  • Kaniadakis entropy becomes multi-additive for these classes.
  • The multi-additivity holds for the composition of two statistically independent and identically distributed distributions.

Conclusions:

  • A novel class of distributions exhibiting multi-additive Kaniadakis entropy has been identified.
  • This research extends the understanding of entropic additivity properties.
  • The findings have potential implications for statistical mechanics and information theory.