By Arieh Ben-Naim
The vital 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 widespread, significant and applicable time period reminiscent of info, lacking info or uncertainty. This substitute might facilitate the translation of the driver of many procedures by way of informational alterations and dispel the secret that has constantly enshrouded entropy.
it's been one hundred forty years due to the fact Clausius coined the time period entropy ; nearly 50 years on the grounds that Shannon built the mathematical idea of knowledge consequently renamed entropy. during this ebook, the writer advocates exchanging entropy via info, a time period that has develop into frequent in lots of branches of technology.
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 proposal of thermodynamics, held before by means of the time period entropy.
the subjects lined contain the basics of likelihood and knowledge concept; the overall inspiration of data in addition to the actual proposal of knowledge as utilized in thermodynamics; the re-derivation of the Sackur Tetrode equation for the entropy of an excellent fuel from simply informational arguments; the elemental formalism of statistical mechanics; and plenty of examples of easy approaches the motive force for that is analyzed when it comes to details.
Contents: parts of likelihood conception; components of data idea; Transition from the final MI to the Thermodynamic MI; The constitution of the rules of Statistical Thermodynamics; a few basic functions.
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In fact, there have been several attempts 1 The usage of the word “belief” in the context of the deﬁnition of probability has led many to deem probability as a subjective concept. This is partially true if we use the term probability colloquially. However, it is not true when probability is used in the sciences. It should be stressed that the probability of an event does not depend on the number of trials; exactly as a mass of a piece of matter does not depend on the number of measurements caried out to determine it.
9. 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.
It is not clear that the property of additivity required from information would also be required for disorder9 ; it might also be meaningless to require the “consistency property” (or the “independence on grouping” — see Chapter 3) from a quantity such as disorder. 1), as claimed by Callen. Moreover, as we shall see in Chapter 3, many of the derived properties of information, such as conditional information, mutual information and the like would not and could not be assigned to disorder. It is unfortunate and perhaps even ironic that Callen dismisses “information” as subjective, while at the same time embracing Shannon’s deﬁnition of information, but renaming it as disorder.