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Entropy of classical histories.

T A Brun1, J B Hartle

  • 1Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

This study explores entropy measures for classical coarse-grained histories, proving inequalities and showing finer-grained descriptions minimize entropy. An extension of the second law of thermodynamics to history entropy is proposed.

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Area of Science:

  • Statistical mechanics
  • Thermodynamics
  • Foundations of physics

Background:

  • Classical coarse-graining of histories is a key concept in statistical mechanics.
  • Jaynes's procedures provide a framework for defining entropy in such systems.
  • Understanding the behavior of entropy with varying levels of detail is crucial.

Purpose of the Study:

  • To analyze and relate different proposals for the entropy of classical coarse-grained histories.
  • To investigate how entropy changes with the degree of coarse-graining.
  • To extend the second law of thermodynamics to encompass the entropy of histories.

Main Methods:

  • Mathematical analysis of entropy measures based on Jaynes's procedures.
  • Derivation of inequalities relating different entropy measures.
  • Examination of entropy as a function of coarse-graining in classical systems.

Main Results:

  • A series of inequalities relating various entropy measures for coarse-grained histories were proven.
  • It was explicitly demonstrated that the finest-grained description minimizes the entropy of a set of histories.
  • An extension of the second law of thermodynamics to the entropy of histories was proposed.

Conclusions:

  • The study provides a rigorous framework for understanding entropy in classical histories.
  • The findings suggest a fundamental principle regarding the relationship between information detail and entropy.
  • The proposed extension of the second law has potential implications for quantum mechanics, particularly consistent histories formulations.

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