Download A Farewell To Entropy: Statistical Thermodynamics Based On by Arieh Ben-Naim PDF
By Arieh Ben-Naim
The imperative message of this e-book is that thermodynamics and statistical mechanics will take advantage of exchanging the unlucky, deceptive and mysterious time period entropy with a extra regular, significant and applicable time period reminiscent of info, lacking info or uncertainty. This alternative might facilitate the translation of the driver of many techniques when it comes to informational alterations and dispel the secret that has continuously enshrouded entropy.
it's been one hundred forty years considering that Clausius coined the time period entropy ; nearly 50 years in view that Shannon built the mathematical idea of data thus renamed entropy. during this booklet, the writer advocates changing entropy by way of info, a time period that has develop into common 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 primary cornerstone inspiration of thermodynamics, held beforehand through the time period entropy.
the subjects lined contain the basics of likelihood and knowledge conception; the final proposal of data in addition to the actual thought of data as utilized in thermodynamics; the re-derivation of the Sackur Tetrode equation for the entropy of an awesome gasoline from simply informational arguments; the basic formalism of statistical mechanics; and plenty of examples of straightforward tactics the motive force for that is analyzed when it comes to info.
Contents: components of likelihood concept; components of knowledge concept; Transition from the overall MI to the Thermodynamic MI; The constitution of the principles of Statistical Thermodynamics; a few easy functions.
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Additional info for A Farewell To Entropy: Statistical Thermodynamics Based On Information
In the left system, we have NA blue, and NB red particles. 3. 6 II 2 V, N 2 V, N Three stages in the process of an expanding ideal gas. 3, as the author did. 4. Mixing of two diﬀerent gases. mixed up in the same volume V . Now, which is more ordered? In my view, the left side is more ordered — all the blues and all the reds are separated in diﬀerent boxes. On the right-hand side, they are mixed up. “Mixed-up” is certainly a disordered state, colloquially speaking. 7). Yet, one can prove that the two systems have equal entropy.
Various thermometers were designed by Ole Christensen 1 2 See, for example, Cooper (1968). We shall use both the notations x and x ¯ for the average of the quantity x. ch01 December 5, 2007 4 B534 Statistical Thermodynamics Based on Information 9in x 6in Statistical Thermodynamics Based on Information Ro/mer (1702), Daniel Gabriel Fahrenheit (1714), Anders Celsius (1742), and many others. Following the invention of the thermometer, it became possible to make precise measurements of the temperature.
By doing that, he actually replaces a well-deﬁned, quantitative and objective quantity by a more subjective concept of disorder. Had Callen not used Shannon’s deﬁnition of information, the concept of disorder would have remained an undeﬁned, qualitative and highly subjective quantity. In my view, it does not make any diﬀerence if you refer to information or to disorder, as subjective or objective. What matters is that order and disorder are not well-deﬁned scientiﬁc concepts. On the other hand, information is a well-deﬁned scientiﬁc quantity, as 9 See examples above.