Are you heading to the good old 2nd law of thermodynamics argument? Because while there is a second law for thermodynamic entropy, there is no second law for informational entropy. Informational entropy is just a statistical quantity with a defining equation similar to thermondynamic energy, but without the laws of thermodynamics around it. Simple pure mathematics.
The matter is discussed in the text: Denbigh and Denbigh [1985].
If you want to play that card, you have to deny the field of probability mathematics.