Based on the book he points to, it goes somewhat like this:
(...) people asked what entropy was microscopically. The answer can be formulated in various ways. The two most extreme answers are:
Entropy measures the (logarithm of the) number π of possible microscopic states. A given macroscopic state can have many microscopic realizations. The logarithm of this number, multiplied by the Boltzmann constant π, gives the entropy.*
Entropy is the expected number of yes-or-no questions, multiplied by π ln 2, the answers of which would tell us everything about the system, i.e., about its microscopic state.
In short, the higher the entropy, the more microstates are possible. Through either of these definitions, entropy measures the quantity of randomness in a system. In other words, entropy measures the transformability of energy: higher entropy means lower transformability. Alternatively, entropy measures the freedom in the choice of microstate that a system has.
(...)
Before we complete our discussion of thermal physics we must point out in another way the importance of the Boltzmann constant π. We have seen that this constant appears whenever the granularity of matter plays a role; it expresses the fact that matter is made of small basic entities. The most striking way to put this statement is the following:
The existence of a characteristic entropy change in nature is a powerful statement. It eliminates the possibility of the continuity of matter and also that of its fractality. A characteristic entropy implies that matter is made of a finite number of small components.
The existence of a characteristic entropy has numerous consequences. First of all, it sheds light on the third principle of thermodynamics. A characteristic entropy implies that absolute zero temperature is not achievable. Secondly, a characteristic entropy explains why entropy values are finite instead of infinite. Thirdly, it fixes the absolute value
of entropy for every system; in continuum physics, entropy, like energy, is only defined up to an additive constant. The quantum of entropy settles all these issues.
(...) people asked what entropy was microscopically. The answer can be formulated in various ways. The two most extreme answers are:
Entropy measures the (logarithm of the) number π of possible microscopic states. A given macroscopic state can have many microscopic realizations. The logarithm of this number, multiplied by the Boltzmann constant π, gives the entropy.*
Entropy is the expected number of yes-or-no questions, multiplied by π ln 2, the answers of which would tell us everything about the system, i.e., about its microscopic state.
In short, the higher the entropy, the more microstates are possible. Through either of these definitions, entropy measures the quantity of randomness in a system. In other words, entropy measures the transformability of energy: higher entropy means lower transformability. Alternatively, entropy measures the freedom in the choice of microstate that a system has.
(...)
Before we complete our discussion of thermal physics we must point out in another way the importance of the Boltzmann constant π. We have seen that this constant appears whenever the granularity of matter plays a role; it expresses the fact that matter is made of small basic entities. The most striking way to put this statement is the following:
There is a characteristic entropy change in nature for single particles: Ξπ β π. This result is almost 100 years old; it was stated most clearly (with a different numerical factor) by Leo Szilard. The same point was made by LΓ©on Brillouin (again with a different numerical factor. The statement can also be taken as the definition of the Boltzmann constant π.
The existence of a characteristic entropy change in nature is a powerful statement. It eliminates the possibility of the continuity of matter and also that of its fractality. A characteristic entropy implies that matter is made of a finite number of small components.
The existence of a characteristic entropy has numerous consequences. First of all, it sheds light on the third principle of thermodynamics. A characteristic entropy implies that absolute zero temperature is not achievable. Secondly, a characteristic entropy explains why entropy values are finite instead of infinite. Thirdly, it fixes the absolute value of entropy for every system; in continuum physics, entropy, like energy, is only defined up to an additive constant. The quantum of entropy settles all these issues.