Chapter

Entropy

Roman Frigg and Charlotte Werndl

in Probabilities in Physics

Published in print September 2011 | ISBN: 9780199577439
Published online September 2011 | e-ISBN: 9780191730603 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199577439.003.0005
Entropy

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This chapter explains the most important notions of entropy and clarifies their interrelations. It furthermore explores what notions of probabilities are at work when entropy is defined in terms of probability. Entropies from thermodynamics, information theory, statistical mechanics, dynamical systems theory, and fractal geometry are surveyed. Notions of entropy from statistical mechanics such as varieties of the Boltzmann and Gibbs entropies can be traced back to information-theoretic entropy. As the chapter points out, an analytic connection between fine-grained Boltzmann entropy and thermodynamic entropy can be established for ideal gases. No easy results about probabilities follow, since several interpretations are compatible with each definition of entropy.

Keywords: probabilities; statistical mechanics; entropy; dynamical systems theory; information theory; thermodynamics

Chapter.  14655 words.  Illustrated.

Subjects: Philosophy of Science

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