Boltzmann Equation for Entropy:
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The third law of thermodynamics states that as a system's temperature approaches absolute zero (0 K), the entropy of the system becomes 0. This is important because it implies that there is an absolute scale for entropy. It also allows us to assume that S=kBln(w)=0 if a system can be prepared in only one way (it is a perfect crystal).
It is also states that the sign of entropy is always positive as long as the system is above absolute zero. This means that entropy in increase and the system is spontaneous as long as the the system is above absolute zero.
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