By Arieh Ben-Naim
The significant message of this booklet is that thermodynamics and statistical mechanics will reap the benefits of exchanging the unlucky, deceptive and mysterious time period entropy with a extra regular, significant and applicable time period similar to details, lacking info or uncertainty. This substitute could facilitate the translation of the motive force of many techniques when it comes to informational alterations and dispel the secret that has regularly enshrouded entropy.
it's been one hundred forty years due to the fact Clausius coined the time period entropy ; virtually 50 years on the grounds that Shannon constructed the mathematical concept of knowledge therefore renamed entropy. during this publication, the writer advocates changing entropy by means of info, a time period that has turn into standard in lots of branches of technological know-how.
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 suggestion of thermodynamics, held before via the time period entropy.
the themes lined comprise the basics of likelihood and knowledge conception; the overall thought 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 amazing gasoline from merely informational arguments; the elemental formalism of statistical mechanics; and lots of examples of straightforward strategies the driver for that is analyzed by way of details.
- Elements of likelihood conception;
- Elements of knowledge thought;
- Transition from the overall MI to the Thermodynamic MI;
- The constitution of the principles of Statistical Thermodynamics;
- Some easy functions.
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Extra info for A farewell to entropy: statistical thermodynamics based on information: S=logW
E. that any deviation from equilibrium will induce a spontaneous process whose eﬀect is to restore the original situation. Suppose for example that thermal ﬂuctuations produce suddenly an increase of temperature locally in a ﬂuid. From the stability condition that CV is positive, and heat will spontaneously ﬂow out from this region (¯ dQ < 0) to lower its temperature (dT < 0). If the stability conditions are not satisﬁed, the homogeneous system will evolve towards a state consisting of two or more portions, called phases, like liquid water and its vapour.
An , Y = Y (A1 , A2 , . . , Ak , Ak+1 , . . 1) ﬁnd a new function for which the derivatives Pi = ∂Y ∂Ai (i = 1, . . 2) will be considered as the independent variables instead of A1 , . . , Ak . The solution is given by k Y [P1 , . . , Pk ] = Y − Pi Ai . 3) results in k dY [P1 , . . 4) k+1 which indicates clearly that Y [P1 , . . , Pk ] is a function of the independent variables P1 , . . , Pk , Ak+1 , . . , An . With Callen (1985), we have used the notation Y [P1 , . . , Pk ] to denote the partial Legendre transformation with respect to A1 , .
D) The maximum of such a curve, deﬁned by the additional condition (∂ 2 p/∂V 2 )T,N = 0, is called the critical point. Show that the values of p, V , and T at the critical point are pc = (1/27)(a/b2 ), Vc = 3bN , Tc = (8/27)(a/bR), respectively. 7. Kelvin’s statement of the second law. Verify that in a reversible transformation at ﬁxed temperature and volume, the maximum reversible work delivered by the system is equal to the decrease of the Helmholtz’s free energy −dF . As an aside result, show that it is not possible to obtain work from an engine operating in a cycle and in contact with one single source of heat.
A farewell to entropy: statistical thermodynamics based on information: S=logW by Arieh Ben-Naim