Nernst argues that if the heat theorem could be violated, then it would be possible to violate the unattainability principle ( Fig. We can understand it as saying that putting a system into its ground state requires infinite time or an infinite number of steps. Here however, we concern ourselves with the question of Nernst’s unattainability principle 8, that Nernst introduced to support his attempted derivations of his heat theorem and counter Einstein’s objections. One can easily find families of Hamiltonians, which satisfy or violate the heat theorem 6, 7. Since we now understand the entropy at zero temperature to be the logarithm of the ground-state degeneracy, the validity of the heat theorem is contingent on whether the degeneracy changes for different parameters of the Hamiltonian. Nernst’s version states that: at zero temperature, a finite size system has an entropy S, which is independent of any external parameters x, that is S( T, x 1)− S( T, x 2)→0 as the temperature T→0. Max Planck’s formulation 3: when the temperature of a pure substance approaches absolute zero, its entropy approaches zero may hold for many crystalline substances, but it is not true in general, and formulations due to Einstein 4 and Nernst 5 were for some time considered to be typically true from an experimental point of view, but sometimes violated.Ī modern understanding of entropy and quantum theory takes the heat theorem outside the realm of thermodynamics. Nernst claimed that he could prove his heat theorem using thermodynamical arguments while Einstein, who refuted several versions of Nernst’s attempted derivation, was convinced that classical thermodynamics was not sufficient for a proof, and that quantum theory had to be taken into account. Walther Nernst’s first formulation of the third law of thermodynamics 1, now called the heat theorem, was the subject of intense discussion 2. The third law of thermodynamics has a controversial past and a number of formulations due to Planck, Einstein and Nernst.
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