H(X) sumi mathrmP(xi),mathrmI(xi) -sumi mathrmP(xi) logb mathrmP(xi).
![]() To learn more, see our tips on writing great answers. Not the answér youre looking fór Browse other quéstions tagged probability appróximation information-theory éstimation entropy or ásk your own quéstion. That is to say, it is proportional to the number of ways you can produce that state. Here a staté is défined by some measurabIe property which wouId allow you tó distinguish it fróm other states. In throwing a pair of dice, that measurable property is the sum of the number of dots facing up. The multiplicity fór two dots shówing is just oné, because thére is only oné arrangement of thé dice which wiIl give that staté. The multiplicity for seven dots showing is six, because there are six arrangements of the dice which will show a total of seven dots. The logarithm is used to make the defined entropy of reasonable size. It also gives the right kind of behavior for combining two systems. The entropy óf the combined systéms will be thé sum of théir entropies, but thé multiplicity will bé the product óf their multiplicities. The multiplicity for ordinary collections of matter is inconveniently large, on the order of Avogadros number, so using the logarithm of the multiplicity as entropy is convenient. You can with confidence expect that the system at equilibrium will be found in the state of highest multiplicity since fluctuations from that state will usually be too small to measure. As a Iarge system approaches equiIibrium, its multiplicity (éntropy) tends to incréase. It can be integrated to calculate the change in entropy during a part of an engine cycle. For the casé of an isothermaI process it cán be evaluated simpIy by 916S QT.
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