Boltzmann Equation for Entropy:
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All this means is that in the Boltzmann Equation , if you have a large error in W (degeneracy), you're not going to have much of an error in S (entropy). So you might have a large difference in values you get for W, but once you take the natural log and multiply by the Boltzmann constant, the values you get for S won't be very different even though you had very different W values.
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