The entropy of perfectly crystalline substances is defined to be zero at absolute zero because there is only one possible microstate available.

Entropy quantifies the number of ways energy can be distributed among the particles of a system. In the case of a perfectly crystalline substance at absolute zero, all particles occupy their lowest energy state. Consequently, there exists only one configuration or arrangement of these particles that corresponds to this state. This single arrangement implies that there is only one possible microstate, denoted as $W = 1$. According to Boltzmann’s entropy formula, given by

$S = k \ln W$

where $S$ represents entropy, $k$ is the Boltzmann constant, and $W$ is the number of microstates, we see that if $W$ equals $1$, then the natural logarithm of $1$ is zero. Thus, the entropy $S$ is also zero.

This principle is encapsulated in the third law of thermodynamics, which asserts that the entropy of a perfect crystal at absolute zero is precisely zero. Absolute zero, defined as $0 \, \text{K}$, represents the lowest possible temperature at which all thermal motion ceases. In a perfect crystal, atoms are arranged in a repeating pattern that extends uniformly in all three spatial dimensions. At absolute zero, each atom remains perfectly stationary in its designated position, resulting in a system devoid of disorder or randomness, and thereby no alternative microstates.

It is crucial to understand that this scenario is idealized. In practice, absolute zero is unattainable, and no crystal can be entirely free of defects. Even at extremely low temperatures, some residual thermal motion and existing imperfections within the crystal structure will invariably contribute to a greater number of possible microstates, leading to a higher entropy. Nonetheless, the third law of thermodynamics serves as a valuable reference point for calculating changes in entropy, establishing a baseline of zero entropy at absolute zero for perfect crystals.