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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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We introduce information temperature for Markov chains using two methods: comparing with Ising chains and analyzing subsequence probabilities. The latter is more versatile for complex chains and applicable to literary texts.

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Area of Science:

  • Information theory
  • Statistical mechanics
  • Computational linguistics

Background:

  • Markov chains model sequential data.
  • Information temperature quantifies information flow.
  • Existing methods for information temperature are limited.

Purpose of the Study:

  • Introduce novel methods for calculating information temperature in Nth-order Markov chains.
  • Compare two distinct approaches for information temperature determination.
  • Extend the concept to weakly correlated Markov chains and analyze literary texts.

Main Methods:

  • Comparing Markov sequences with equilibrium Ising chains.
  • Utilizing probabilities of finite-length subsequences to determine entropy.
  • Calculating information temperature as the derivative of entropy with respect to energy.
  • Analyzing stepwise and power memory functions for one-parametric Markov chains.

Main Results:

  • Both proposed methods yield similar results for nearest-neighbor interactions.
  • The Ising chain comparison method becomes complex for N>3.
  • Information temperature was successfully applied to literary texts, demonstrating practical utility.

Conclusions:

  • Two viable methods for information temperature calculation in Markov chains are presented.
  • The subsequence probability method offers greater flexibility for higher-order chains.
  • The developed framework has potential applications in analyzing complex data, including natural language.