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partition function |
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Symbol Z. For a thermodynamic system with energy levels E{TAG(tag=>sub)}i{TAG}, the partition function (a function of T or, for simplicity, of β = 1/kT, where T is the thermodynamic temperature and k is the Boltzmann constant) is defined as
{img src=show_image.php?name=image_16_09.gif }
This is a very important concept in statistical mechanics since this form of Z is recognizable as the normalizing denominator in the calculation of, for example, the mean energy:
{img src=show_image.php?name=image_16_10.gif }
With a little algebra this leads to the conclusion that Ē = -∂Z/∂β and all the other thermodynamic functions such as entropy and free energy can be expressed in terms of Z and its derivatives. Thus the function Z(β) contains all the information relevant to the thermodynamics of the system. |
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