Thermodynamics And Statistical Mechanics

A Farewell To Entropy by Arieh Ben-Naim

By Arieh Ben-Naim

The relevant message of this booklet is that thermodynamics and statistical mechanics will reap the benefits of changing the unlucky, deceptive and mysterious time period “entropy” with a extra general, significant and applicable time period akin to info, lacking details or uncertainty. This substitute might facilitate the translation of the “driving strength” of many strategies by way of informational alterations and dispel the secret that has continuously enshrouded entropy. it's been a hundred and forty years due to the fact that Clausius coined the time period “entropy” virtually 50 years considering the fact that Shannon constructed the mathematical conception of “information” - for that reason renamed “entropy”. during this booklet, the writer advocates exchanging “entropy” by way of “information”, a time period that has develop into customary in lots of branches of technological know-how. the writer additionally takes a brand new and ambitious method of thermodynamics and statistical mechanics. details is used not just as a device for predicting distributions yet because the primary cornerstone thought of thermodynamics, held previously by way of the time period “entropy”. the themes coated comprise the basics of likelihood and data thought; the final suggestion of knowledge in addition to the actual thought of data as utilized in thermodynamics; the re-derivation of the Sackur-Tetrode equation for the entropy of a terrific gasoline from basically informational arguments; the basic formalism of statistical mechanics; and lots of examples of easy approaches the “driving strength” for that is analyzed when it comes to details.

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I have taught thermodynamics for many years and used Callen’s book as a textbook. It is an excellent book. However, with all due respect to Callen and to his book, I must say that Callen misleads the reader with these statements. Shannon never defined nor referred to “disorder” in his writings. In my opinion, Callen is ch01 December 5, 2007 B534 Statistical Thermodynamics Based on Information Introduction 9in x 6in 17 fudging with the definition of disorder in the quoted statement and in the rest of that chapter.

In fact, no one has claimed that either of these is subjective. The subjectivity of information enters only when we apply the concept of information in its broader sense. Jaynes pioneered the application of information theory to statistical mechanics. In this approach, the fundamental probabilities of statistical mechanics (see Chapter 5) are obtained by using the principle of maximum entropy. This principle states that the equilibrium distributions are obtained by maximizing the entropy (or the MI) with respect to all other distributions.

Velocity distributions for a gas at different temperatures. (a) The distributions corresponding to the left-hand side of Fig. 8. (b) The overall distribution of velocities, before and after the process of heat transfer. ch01 December 5, 2007 B534 Statistical Thermodynamics Based on Information 9in x 6in Introduction 15 distribution is more ordered or disordered? Can you tell in which distribution the spread of kinetic energy is more even, or over a larger range of velocities? To me, the final distribution (the dashed curve) looks more ordered, and the distribution looks less spread out over the range of velocities.

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