The entropy if there are n equally probable states but the actual state is undetermined is S = k ln n, where k is Boltzmann's constant. If the number of zones is clipped to less than 19, the entropy of the system will be decreased accordingly. The Second Law of Thermodynamics imposes an entropy cost for the clipping, so according to the Second Law the entropy of the surroundings must increase by at least as much. At temperature T, if the total entropy increases by delta S, work of at most T delta S can be extracted. At temperature T, work of at least T delta S must be performed to decrease the entropy of a system by delta S. The performance of this work requires an increase in the entropy of the surroundings of at least delta S.

When you speak about maximum entropy value if Information Entropy aka Shannon entropy, it is the white noise whatever it means in your system or model.

I = - Sum_1_N (p * log_b(p))

where p is the probability of a given event and 'b' is base, which usually has the value of 2 or 'e'. 'N' is the number of possible states of the system.

* system is in one state, it means p=1 and I = 0.

* system is equilibrium p = 1/N and I = max. This state is often called white noise.

Basically, as the system becomes visiting more equally ball of its states, it is reaching its maximum of entropy.

The actual value depends on all parameters used.

Remark: Shannon used base 'b' because it gives you a direct answer about the strength of use encoding. Strong encodings get high entropy and a weak low one.

Examples:

p = 0.5, 0.5: I = 0.6931...

p = 0.9, 0.1: I = 0.1355...

p = 0.25, 0.25, 0.25, 0.25: I = 5.5452

What we see is:

* Equal probabilities gives the highest entropy. White noise. Unequal probabilities are always lower for given N.

* With an increasing number of parts/boxes/states N the max value of entropy increases.

Hopefully, this helps a bit.

Information and entropy can be measured in different units. If the unit is a bit the maximal entropy is log_2 (n) where log_2 denotes the logarithm with base 2. If the unit is a nat (natural unit) the maximum entropy is ln(n). If the unit is a digit the maximum entropy is log(n). In thermodynamics others units are used, but one can easily convert between all these different units.

The Boltzmann entropy is S=KlnW where K is Boltzmann constant and W is the number of microstates. Since each bit can be one or zero, therefore, W=2^N where N is the number of bits. The entropy is therefore S=KNln2. In information theory, Kln2 is considered as one and the entropy is S=N bits. The definition of a bit is, therefore, the probability of 50% to find an oscillator.