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We argue that a very large class of quantum pure states of isolatedmacroscopic bodies have sharply peaked energy distributions, with their widthrelative to the average scaling between $\sim N^{-1}$ and $\sim N^{-1/2}$, with$N \gg 1$, the number of atoms conforming the body. Those states are densesuperpositions of energy eigenstates within arbitrary finite or infinite energyintervals that decay sufficiently fast. The sharpness of the energydistribution implies that closed systems in those states are {\itmicrocanonical} in the sense that only energy eigenstates very near to the meanenergy contribute to their thermodynamic evolution. Since thermodynamicsaccurately describes processes of macroscopic bodies and requires that closedsystems have constant energy, our claim is that these pure states are typicalof macroscopic systems. The main assumption beneath the energy sharpness isthat the isolated body can reach thermal equilibrium if left unaltered. Weargue that such a self-sharpness of the energy in macroscopic bodies indicatesthat the First Law of Thermodynamics is statistical in character.

Sharp energy self-determination of macroscopic quantum bodies in pure states, as a validation of the First Law of Thermodynamics