High Quality Content by WIKIPEDIA articles! In thermodynamics, particularly statistical mechanics, the thermodynamic limit is reached as the number of particles (atoms or molecules) in a system, N, approaches infinity — in practical terms, one mole of substance or Avogadro's number ? 6x1023 of particles. The thermodynamic behavior of a system is asymptotically approximated by the results of statistical mechanics as N tends to infinity, and calculations using the various ensembles used in statistical mechanics converge. The mathematical basis of this result comes from manipulating factorials arising from Boltzmann's formula for the entropy, S = k log W by using Stirling's approximation, which is justified only when applied to large numbers. Empirically, the relative size of fluctuations from the average is much bigger from collections of only a few atoms or molecules, and so the probabilistic assumptions of statistical mechanics break down.

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