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Entropy02:39

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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 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.
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Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
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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. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
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Entropy and long-range memory in random symbolic additive Markov chains.

S S Melnik1, O V Usatenko1

  • 1A. Ya. Usikov Institute for Radiophysics and Electronics Ukrainian Academy of Science, 12 Proskura Street, 61805 Kharkov, Ukraine.

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This study estimates the entropy of random symbolic sequences using a Markov chain model. The research quantifies entropy contributions from correlation and fluctuation, applicable to text and DNA sequences.

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Area of Science:

  • Information Theory
  • Statistical Mechanics
  • Computational Biology

Background:

  • Entropy quantifies uncertainty in random symbolic sequences.
  • Previous models often simplify complex memory dependencies.

Purpose of the Study:

  • Develop an entropy estimation method for finite alphabet symbolic sequences.
  • Model sequences using high-order additive stationary ergodic Markov chains with long-range memory.

Main Methods:

  • Utilized symbolic pair correlation functions to express conditional entropy.
  • Developed an algorithm for estimating conditional entropy in finite sequences.
  • Analyzed contributions to entropy as correlation and fluctuation.

Main Results:

  • Derived analytical results for entropy estimation.
  • Quantified entropy contributions from correlation and fluctuation.
  • Applied the method to written English and DNA nucleotide sequences.

Conclusions:

  • The developed theory provides a sophisticated approach for systems with mixed memory ranges.
  • Enables more accurate entropy estimation in diverse symbolic sequences.
  • Opens avenues for advanced system description in computational and statistical fields.