By Arieh Ben-Naim
The significant message of this ebook is that thermodynamics and statistical mechanics will make the most of exchanging the unlucky, deceptive and mysterious time period entropy with a extra customary, significant and applicable time period akin to info, lacking info or uncertainty. This substitute might facilitate the translation of the motive force of many strategies by way of informational adjustments and dispel the secret that has continually enshrouded entropy.
it's been one hundred forty years given that Clausius coined the time period entropy ; virtually 50 years when you consider that Shannon constructed the mathematical thought of knowledge accordingly renamed entropy. during this e-book, the writer advocates changing entropy by means of info, a time period that has turn into universal in lots of branches of technology.
the writer additionally takes a brand new and impressive method of thermodynamics and statistical mechanics. details is used not just as a device for predicting distributions yet because the primary cornerstone proposal of thermodynamics, held formerly through the time period entropy.
the themes coated contain the basics of likelihood and knowledge concept; the overall inspiration of data in addition to the actual inspiration of data as utilized in thermodynamics; the re-derivation of the Sackur Tetrode equation for the entropy of a terrific fuel from simply informational arguments; the elemental formalism of statistical mechanics; and lots of examples of easy tactics the motive force for that's analyzed when it comes to details.
Contents: components of likelihood conception; components of knowledge conception; Transition from the overall MI to the Thermodynamic MI; The constitution of the rules of Statistical Thermodynamics; a few basic purposes.
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Extra resources for A Farewell To Entropy: Statistical Thermodynamics Based On Information
15) or equivalently T = m v2 . 16) Hence A=N =N m v2 m v2 −N S/N 2 3 m v2 2 1− 2S . 17) includes the entropy, or rather the missing information (M I). Since S is an extensive quantity, S/N is the M I per particle in this system. 2 The Association of Entropy with Disorder During over a hundred years of the history of entropy, there have been many attempts to interpret and understand entropy. We shall discuss the two main groups of such interpretations of entropy. The earliest, and nowadays, the most common interpretation of the entropy is in terms of disorder, or any of the related concepts such as “disorganization,” “mixed-upness,” “spread of energy,” “randomness,” “chaos” and the like.
It is clear from this sequence of events that the units of temperature were determined at least two decades before the recognition and acceptance of the molecular interpretation of the temperature. When Clausius formulated the Second Law in terms of dQ/T , it was only natural to deﬁne the entropy in units of energy divided by temperature. , energy divided by temperature or Joule/Kelvin, or J/K. 10) (instead of 3kB T /2 on the right-hand side). 11) or on the deﬁnition of Clausius’ entropy, dQ . 12) T The only diﬀerence would have been that the entropy S would now be a dimensionless quantity.
There is of course a conceptual diﬃculty in identifying the Boltzmann entropy with the Clausius entropy. However, it has been shown in numerous examples that changes in one concept are equivalent to changes in the other, provided that the constant k is chosen as the Boltzmann constant, with the dimensions of energy over absolute temperature (K). Once one accepts the identiﬁcation of the Clausius entropy with the Boltzmann entropy, then the interpretation of the entropy as uncertainty, information or MI is inevitable.