10: Entropy and Information

Thermodynamics and Statistical Mechanics · LibreTexts

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    From LibreTexts, under CC BY-NC-SA 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    The concept of entropy is one of the more difficult concepts in physics. Historically, it emerged as a consequence of the second law of thermodynamics, as in Equation 3.4.13. Later, Boltzmann gave a general definition for it in terms of the number of ways of distributing a given number of particles, as in Equation 7.2.3. But a clearer understanding of entropy is related to its interpretation in terms of information. We will briefly discuss this point of view here.

    • 10.1: Information
      We want to give a quantification of the idea of information. This is originally due to C. Shannon.
    • 10.2: Maxwell’s Demon
      There is a very interesting thought experiment due to Maxwell which is perhaps best phrased as a potential violation of the second law of thermodynamics. The resolution of this problem highlights the role of entropy as information.
    • 10.3: Entropy and Gravity
      There is something deep about the concept of entropy which is related to gravity. This is far from being well understood, and is atopic of ongoing research, but there are good reasons to think that the Einstein field equations for gravity may actually emerge as some some sort of entropy maximization condition. A point of contact between gravity and entropy is for spacetimes with a horizon, an example being a black hole.

    This page titled 10: Entropy and Information was last modified on Sun, 28 Mar 2021 02:05:19 GMT and is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by V. Parameswaran Nair via source content that was edited to the style and standards of the LibreTexts platform.