By Arieh Ben-Naim
The critical message of this ebook is that thermodynamics and statistical mechanics will take advantage of changing the unlucky, deceptive and mysterious time period entropy with a extra common, significant and applicable time period comparable to details, lacking info or uncertainty. This alternative could facilitate the translation of the driver of many methods by way of informational alterations and dispel the secret that has consistently enshrouded entropy.
it's been one hundred forty years because Clausius coined the time period entropy ; nearly 50 years due to the fact Shannon built the mathematical thought of data hence renamed entropy. during this publication, the writer advocates changing entropy via info, a time period that has develop 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 primary cornerstone idea of thermodynamics, held beforehand via the time period entropy.
the themes lined comprise the basics of likelihood and knowledge idea; the final proposal of data in addition to the actual suggestion of data as utilized in thermodynamics; the re-derivation of the Sackur Tetrode equation for the entropy of an awesome gasoline from in simple terms informational arguments; the elemental formalism of statistical mechanics; and plenty of examples of easy strategies the driver for that's analyzed by way of info.
- Elements of likelihood idea;
- Elements of data concept;
- Transition from the overall MI to the Thermodynamic MI;
- The constitution of the rules of Statistical Thermodynamics;
- Some uncomplicated functions.
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Additional info for A farewell to entropy: statistical thermodynamics based on information: S=logW
Iky pxi pyi exp …iky yi † ‡ yij Fxij exp …iky yi † 2 i; j iky yij i ² iky Pyx …ky ; t†: …6:6† In this equation Fxij is the x-component of the force exerted on particle i by particle j, yij ² yj ¡ yi and Pxy is the xy-component of the pressure tensor. We now consider the response of the pressure tensor to a strain rate, ®, applied to the ¯uid for t > 0 in the causal system and for t < 0 in the anticausal system. In the causal system the strain rate is turned on at t ˆ 0 while in the anticausal system the strain rate is turned o at t ˆ 0.
6. 12). 2 shows the response of Pxy for a trajectory and its conjugate when a constant strain rate is applied. The response was determined using non-equilibrium molecular dynamics simulations of 200 discs in two Cartesian dimensions. The discs interact via the WCA potential , ( 4…r¡12 ¡ r¡6 † ‡ 1 r < 21=6 …6:29† ¿…r† ˆ 0 r > 21=6 : Shearing periodic boundary conditions were used to minimize boundary e ects . The system was maintained at a constant kinetic temperature of T ˆ 1:0 and the particle density was n ˆ N=V ˆ 0:8.
We need to know initial or logically, ®nal conditions. When we model laboratory experiments we require initial conditions because this is precisely how the experiments are conducted and because initially, the ®nal state of the system is generally not known. Although we can mimic the e ects of time ¯owing backwards (time decrementing) by applying a time reversal mapping to a set of phases, time nevertheless evolves in a positive sense. Indeed the e ectiveness of the time reversal mapping relies on the fact that time only increases.
A farewell to entropy: statistical thermodynamics based on information: S=logW by Arieh Ben-Naim