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Read e-book online A farewell to entropy: statistical thermodynamics based on PDF

By Arieh Ben-Naim

ISBN-10: 9812707069

ISBN-13: 9789812707062

The significant message of this ebook is that thermodynamics and statistical mechanics will take advantage of exchanging the unlucky, deceptive and mysterious time period entropy with a extra frequent, significant and applicable time period reminiscent of info, lacking info or uncertainty. This substitute could facilitate the translation of the driver of many procedures by way of informational adjustments and dispel the secret that has regularly enshrouded entropy.

it's been one hundred forty years in view that Clausius coined the time period entropy ; virtually 50 years given that Shannon built the mathematical concept of data as a result renamed entropy. during this publication, the writer advocates changing entropy via details, a time period that has develop into general in lots of branches of technological know-how.

the writer additionally takes a brand new and impressive method of thermodynamics and statistical mechanics. info is used not just as a device for predicting distributions yet because the basic cornerstone suggestion of thermodynamics, held earlier by way of the time period entropy.

the themes lined comprise the basics of chance and data conception; the final inspiration of data in addition to the actual thought of knowledge as utilized in thermodynamics; the re-derivation of the Sackur Tetrode equation for the entropy of a fantastic fuel from in simple terms informational arguments; the basic formalism of statistical mechanics; and lots of examples of straightforward methods the driver for that is analyzed by way of details.

Contents:

  • Elements of likelihood thought;
  • Elements of knowledge concept;
  • Transition from the overall MI to the Thermodynamic MI;
  • The constitution of the rules of Statistical Thermodynamics;
  • Some basic functions.

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Extra resources for A farewell to entropy: statistical thermodynamics based on information: S=logW

Sample text

DStot has to be zero for all directions: If we change only Ug , but keep Ul , Vg , Ni,g and Ni,l constant, dStot has still to be zero. dStot = 1 1 dUg , − Tg Ts dUg = 0 → Tg = Ts . Similarly, if we change only Ul we get Tl = Ts (= Tg ). 4) NOTE: “All directions”-reasoning is only possible if variables Ug , Ul , Vg , Ni,g and Ni,l are independent; one of them can be changed without affecting the others. All the constraints have been used before eq. 1). For example set 18 2 Phase equilibrium Ug , Ul , Vg , Vl ,Ni,g and Ni,l are not independent.

For example set 18 2 Phase equilibrium Ug , Ul , Vg , Vl ,Ni,g and Ni,l are not independent. We have to get rid of Vg or Vl before applying the trick. The conclusion is that the chemical potentials, temperature and pressure have to be same in all the phases, also the surface phase. Generally in equilibrium temperature and chemical potentials have to be constant in space and time. Otherwise heat or particles flow. Pressure has to be constant in time, but not in space as we shall soon see. h Fig. 2.

We manipulate the chemical potential of the vapour by assuming that the mixture of vapours is an ideal mixture. This means that each component behaves as if it was alone with total pressure equal to the partial pressure p (P ) be the chemical of that component, Pi,g = xi,g Pg . Let µpi,g (P ) and vi,g potential and partial molecular volume of an independent (pure) vapour i at pressure P . 17) Pi,x where Pi,x is so far arbitrary vapour pressure. Now we select liquid pressure Px and vapour pressure Pi,x so that component i of the vapour is in equilibrium with the liquid in a flat surface case, µi,l (Px , xi,l ) = µpi,g (Pi,x ).

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A farewell to entropy: statistical thermodynamics based on information: S=logW by Arieh Ben-Naim


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