The answer is simply that a random number generator's entropy and Thermodynamic entropy are not the same things.

A couple of distinguishing features of thermodynamic entropy is the following.

• Every thermodynamic entropy depends on a variable corresponding to the thermodynamic energy of the system.
• Thermodynamic entropies are defined on equilibrium states of macroscopic systems.

In the absence of these two conditions, whatever concept we give the name of entropy will be useless as a thermodynamic quantity. Said in another way, non-thermodynamic entropies are completely decoupled from thermodynamics.

Nothing prevents us from associating the name of entropy with one or more concepts connected to random number generators (RNG). For instance, we can associate an RNG with Shannon's or Kolmogoroff's entropies (that are conceptually different entropies). However, no established or reasonable concept of equilibrium can be associated with RNGs, and there is no energy they depend on. We could say that we have a composite system consisting of the material the computer is made of and the RNG and that the total entropy is the sum of the thermodynamic entropy of the hardware plus Kolmogoroff's (or Shannon's) entropy of RNG. However, that's all. There is no way to speak about a redistribution of energy maximizing the total entropy.

Notice that the decoupling between different entropies does not mean that the common features of different entropy definitions can't help to shed light on the concept itself.

The answer is simply that a random number generator's entropy and Thermodynamic entropy are not the same things.

A couple of distinct features of thermodynamic entropy is the following.

• Every thermodynamic entropy depends on a variable corresponding to the thermodynamic energy of the system.
• Thermodynamic entropies are defined for equilibrium states of macroscopic systems.

In the absence of these two conditions, whatever concept we give the name of entropy will be useless as a thermodynamic quantity. Said in another way, non-thermodynamic entropies are entirely decoupled from thermodynamics.

Nothing prevents us from associating the name of entropy with one or more concepts connected to random number generators (RNG). For instance, we can associate an RNG with Shannon's or Kolmogoroff's entropies (conceptually different entropies). However, no established or reasonable concept of equilibrium can be associated with RNGs, and there is no energy they depend on. We could say that we have a composite system consisting of the material the computer is made of and the RNG, and that the total entropy is the sum of the thermodynamic entropy of the hardware plus Kolmogoroff's (or Shannon's) entropy of RNG. However, that's all. There is no way to speak about a redistribution of energy maximizing the total entropy.

Notice that the decoupling between different entropies does not mean that the common features of the two definitions can't help shed light on the concept itself.