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A typical application is the calculation of a thermodynamic potential from a partition function. These functions often contain terms with factorials n ! {\displaystyle n!} which scale as n 1 / 2 n n / e n {\displaystyle n^{1/2}n^{n}/e^{n}} ( Stirling's approximation ).
The initial idea is usually attributed to the work of Hardy with Srinivasa Ramanujan a few years earlier, in 1916 and 1917, on the asymptotics of the partition function.It was taken up by many other researchers, including Harold Davenport and I. M. Vinogradov, who modified the formulation slightly (moving from complex analysis to exponential sums), without changing the broad lines.
The partition function is commonly used as a probability-generating function for expectation values of various functions of the random variables. So, for example, taking β {\displaystyle \beta } as an adjustable parameter, then the derivative of log ( Z ( β ) ) {\displaystyle \log(Z(\beta ))} with respect to β {\displaystyle \beta }
It may not be obvious why the partition function, as we have defined it above, is an important quantity. First, consider what goes into it. The partition function is a function of the temperature T and the microstate energies E 1, E 2, E 3, etc. The microstate energies are determined by other thermodynamic variables, such as the number of ...
The San Francisco 49ers suspended linebacker De’Vondre Campbell for the rest of the regular season after he refused to enter a game after losing his starting job. General manager John Lynch ...
The required output is a partition of S into k subsets, such that the sums in the subsets are as nearly equal as possible. Greedy algorithms process the numbers sequentially, and insert the next number into a bin in which the sum of numbers is currently smallest.
The number of men who have developed breast cancer while working or living around Ground Zero has skyrocketed, The Post has learned. The federal Centers for Diseases Control reports that 91 men in ...
New York Giants quarterback Tommy DeVito is officially inactive for Thursday's Thanksgiving game against the Dallas Cowboys (4:25 p.m. ET, Fox) due to a forearm injury.