By Arieh Ben-Naim
The central message of this booklet is that thermodynamics and statistical mechanics will make the most of exchanging the unlucky, deceptive and mysterious time period entropy with a extra standard, significant and applicable time period reminiscent of info, lacking info or uncertainty. This alternative might facilitate the translation of the driver of many approaches by way of informational alterations and dispel the secret that has constantly enshrouded entropy.
it's been one hundred forty years for the reason that Clausius coined the time period entropy ; nearly 50 years considering Shannon built the mathematical concept of knowledge for that reason renamed entropy. during this ebook, the writer advocates exchanging entropy via info, a time period that has turn into everyday in lots of branches of technology.
the writer additionally takes a brand new and ambitious method of thermodynamics and statistical mechanics. info is used not just as a device for predicting distributions yet because the basic cornerstone idea of thermodynamics, held earlier through the time period entropy.
the subjects coated contain the basics of likelihood and data idea; the final thought of data in addition to the actual suggestion of knowledge as utilized in thermodynamics; the re-derivation of the Sackur Tetrode equation for the entropy of an incredible fuel from only informational arguments; the basic formalism of statistical mechanics; and lots of examples of easy techniques the motive force for that is analyzed by way of info.
Contents: components of likelihood thought; components of knowledge thought; Transition from the final MI to the Thermodynamic MI; The constitution of the rules of Statistical Thermodynamics; a few easy purposes.
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Additional info for A Farewell To Entropy: Statistical Thermodynamics Based On Information
The same principle can be applied to derive the most non-commital, or the least biased, distribution that is consistent with all the given information. This is a very general principle that has a far more general applicability. See also Chapters 4–6. ” “. . we accept the von-Neumann–Shannon expression for entropy, very literally as a measure of the amount of uncertainty represented by the probability distribution; thus entropy becomes the primitive concept. . , Friedman and Shimony (1971) and Diaz and Shimony (1981).
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.
On the other hand, information or MI is adequate. As we shall see in Chapter 6, the increase in the entropy in this process can be interpreted as an increase in the MI. It will be shown that the ﬁnal distribution of velocities is that with the minimum Shannon’s information or maximum MI. Although this result cannot be seen by looking directly at the system, nor by looking at the velocity distribution curves, it can be proven mathematically. Order and disorder are vague and highly subjective concepts.
A Farewell To Entropy: Statistical Thermodynamics Based On Information by Arieh Ben-Naim