Third law of thermodynamics
The third law of thermodynamics (or Nernst's theorem after the experimental work of Walther Nernst in 1906 ) states that the entropy of a system approaches a minimum (that of its ground state) as one approaches the temperature of absolute zero. One can write
where is the number of particles. Note that there are systems whose ground state entropy is not zero, for example metastable states or glasses, or systems with weakly or non-coupled spins that are not subject to an ordering field.
thus as , otherwise the integrand would become infinite.
Similarly for the thermal expansion coefficient
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