How can I measure the entropy of a system with continuous deterministic variables without knowing their PDF?

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Let's say I have 1 input variable that can take any real value from the environment, and 8 internal variables that are affected by the input and among themselves. As python variables they can take values as high/low as your memmory allows, but i don't know their PDF in principle.

Does it make sense to measure entropy of such a deterministic system? How? Should I consider the input variable as random to measure it? If that is the case, I do not know its frequencies/density. I am aware of differential entropy and limiting density of discrete points (LDDP),but it needs the PDF. Could other measures be calculated (e.g. mutual information between the environment and the internal system)?

I am a programmer and this stuff is tricky for me :)