By Arieh Ben-Naim
The central message of this publication is that thermodynamics and statistical mechanics will take advantage 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 strategies by way of informational alterations and dispel the secret that has consistently enshrouded entropy.
it's been a hundred and forty years seeing that Clausius coined the time period entropy ; nearly 50 years on the grounds that Shannon constructed the mathematical idea of knowledge therefore renamed entropy. during this e-book, the writer advocates exchanging entropy by means of info, a time period that has develop into accepted 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 notion of thermodynamics, held earlier via the time period entropy.
the subjects lined comprise the basics of likelihood and data idea; the final thought of knowledge in addition to the actual thought of knowledge as utilized in thermodynamics; the re-derivation of the Sackur Tetrode equation for the entropy of an amazing gasoline from only informational arguments; the elemental formalism of statistical mechanics; and lots of examples of easy tactics the motive force for that is analyzed by way of info.
- Elements of chance thought;
- Elements of knowledge idea;
- Transition from the final MI to the Thermodynamic MI;
- The constitution of the rules of Statistical Thermodynamics;
- Some easy functions.
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Additional resources for A farewell to entropy: statistical thermodynamics based on information: S=logW
13 on page 16. We can similarly define the Gibbs free energy of dilution or mixing by substituting this equation into the definition of ∆G°: C ∆G dil = ∆H dil – RT ln -----1- C 2 (24) If the substance in question forms an ideal solution with the other components, then ∆Hdil is by definition zero, and we can write1 C2 ∆G dil = RT ln ------ C1 (25) These relations tell us that the dilution of a substance from an initial concentration C1 to a more dilute concentration C2 is accompanied by a decrease in the free energy, and thus will occur spontaneously.
Those that did not adapt to this new environment have literally “gone underground” and constitute the more primitive anaerobic bacteria. The function of oxygen in respiration is to serve as an acceptor of the electrons that glucose loses when it undergoes oxidation. Other electron acceptors can fulfill the same function when oxygen is not available, but none yields nearly as much free energy. For example, if oxygen cannot be supplied to mammalian muscle cells as rapidly as it is needed, they switch over to an anaerobic process yielding lactic acid instead of CO2: C6H12O6 + 2 ADP → 2 CH3CH(OH)COOH ∆G° = –218 kJ mol–1 In this process, only (2 × 30 kJ) = 60 kJ of free energy is captured, so the efficiency is only 28% on the basis of this reaction, and it is even lower in relation to glucose.
So the sign of the entropy change determines whether the reaction becomes more or less allowed as the temperature increases. We often want to know how a change in the temperature will affect the value of an equilibrium constant whose value is known at some fixed temperature. Suppose that the equilibrium constant has the value K1 at temperature T1 and we wish to estimate K2 at temperature T2. Expanding Eq. 35 in terms of ∆H° and ∆S°, we obtain –RT1 ln K1 = ∆H ° – T1 ∆S° and –RT2 ln K2 = ∆H ° – T2 ∆S° Dividing both sides by RT and subtracting, we obtain Free energy: the Gibbs function Page 34 ∆H° ∆H° ln K 1 – ln K 2 = – ----------- + ----------- RT 1 RT 2 (39) Which is most conveniently expressed as the ratio K1 ∆H° 1 1 ln ------ = – ----------- ----- – ----- K2 R T1 T2 (40) Do you remember the Le Châtelier Principle?
A farewell to entropy: statistical thermodynamics based on information: S=logW by Arieh Ben-Naim