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However, it is useful as an intermediate step to calculate multiplicity as a function of and . This approach shows that the number of available macrostates is N + 1 . For example, in a very small system with N = 2 dipoles, there are three macrostates, corresponding to N ↑ = 0 , 1 , 2. {\displaystyle N_{\uparrow }=0,1,2.}
The dimension p of the p × p transfer matrix equals the number of states the subsystem may have; the transfer matrix itself W k encodes the statistical weight associated with a particular state of subsystem k − 1 being next to another state of subsystem k.
For typical applications in nuclear physics, where one particle's mass is much larger than the other the reduced mass can be approximated as the smaller mass of the system. The limit of the reduced mass formula as one mass goes to infinity is the smaller mass, thus this approximation is used to ease calculations, especially when the larger ...
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is a weighted sum or weighted average .
In mathematics, more specifically in the theory of Monte Carlo methods, variance reduction is a procedure used to increase the precision of the estimates obtained for a given simulation or computational effort. [1] Every output random variable from the simulation is associated with a variance which limits the precision of the simulation results.
In statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD) in isotopic dating [1] and variance of unit weight in the context of weighted least squares. [2] [3]
In contrast, the macrostate of a system refers to its macroscopic properties, such as its temperature, pressure, volume and density. [1] Treatments on statistical mechanics [2] [3] define a macrostate as follows: a particular set of values of energy, the number of particles, and the volume of an isolated thermodynamic system is said to specify ...
Right: The reduction in flux passing through a surface can be visualized by reduction in F or dS equivalently (resolved into components, θ is angle to normal n). F •d S is the component of flux passing through the surface, multiplied by the area of the surface (see dot product ).