[Hermel]

Not really. Even from a point of view of an experimenter with perfect information, the entropy of the system declines over time as fewer and fewer bits are needed to describe the system.

For example, start with a Glas of warm water and an ice cube in it. Over time, the ice will melt and the range of different temperatures of the molecules decline. Consequently, you need fewer and fewer bits to describe the complete state of the system. It takes fewer Bits to encode all the velocities of a million molecules that all move at a similar speed than to encode all the velocities of a million molecules that move at very different speeds.

The more similar the state of the molecules becomes, the shorter a text becomes that has to describe the complete state of a system. Therefore, entropy is decreasing even from the point of view of an observer with perfect information.

[Ombudsman]

Because ice is solid you can argue it takes less information because the particles aren't moving at all or in together in unison, so it will take less buts to encode.

Furthermore, velocity is also a product of direction as much as speed, so if you take into consideration a solid object may vibrate it's particles in the same direction while a liquid can have it's particles in infinite directions, you're talking about way more information you have to encode.

[leereeves]

What is perfect information?

I understood perfect information to include infinite precision knowledge of non-quantized values like position and momentum. To store that information we'd almost always need infinite bits to express the state of even one particle.

(...and cough ignoring uncertainty...)

Using a finite number of bits was described in the comment above as "lumping positions into pixels".

[trenchgun]

Surely glass of warm water + ice cube is lower entropy state compared to melted icecube mixed in the water.