# Does the ergodic hypothesis provide a uniquely determined definition of entropy?

One can distinguish between two schools of thought regarding thermodynamic entropy:

(a) Thermodynamic entropy is a measure of the "amount of hidden information" in a system. Therefore, the entropy depends on which information we consider to be "hidden". (If we have god-like powers of observation and we can see the position and velocity of every particle, then the entropy is zero).

(b) Assuming that the ergodic hypothesis holds, then the thermodynamic entropy is the logarithm of the phase space volume which an ergodic system explores. Therefore, entropy is completely determined by the physics.

Are these two points of view fundamentally incompatible? Which one gives the correct experimental predictions?

Note: this is slightly different from other questions about whether the entropy is subjective, such as

Entropy : subjective lack of knowledge that leads to objective conclusions

There is an "objective" way to define entropy in school (a), namely the hidden information is the one we are unable to access. The question is whether the thermodynamic entropy thus depends on our capabilities (which is not the same as depending on our beliefs).