In statistical mechanics, the statistical weight is the relative probability (possibly unnormalized) of a particular feature of a state. If the energy associated with the feature is ΔE, the statistical weight is given by the Boltzmann factor e-ΔE/kT, where k is the Boltzmann constant and T is the temperature in kelvin.
The statistical weight is a convenient shorthand that is often used in transfer matrix solutions of problems in statistical mechanics.
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“Not the less does nature continue to fill the heart of youth with suggestions of his enthusiasm, and there are now men,—if indeed I can speak in the plural number,—more exactly, I will say, I have just been conversing with one man, to whom no weight of adverse experience will make it for a moment appear impossible, that thousands of human beings might exercise towards each other the grandest and simplest of sentiments, as well as a knot of friends, or a pair of lovers.”
—Ralph Waldo Emerson (1803–1882)