What is entropy and what is information?

I'm taking it as a given - since this is only a mental experiment - each of the gazillion set ups is equal in energy content

I'm not going to manipulate any of the gazillion cubes

They are phantom images only

Hence each mental image is at resting state

Which is why this manipulating into another of the gazillion representations is NOT repeat NOT suitable to explain entropy since EACH of the states are equal

REPEAT with minor correction

Entropy needs the object to move to a lower energy level

To reverse the entropy requires energy to be pumped back into the object

In doing that you cause the object you are pumping the energy from to under go entropy

Taking a real cube (not a mental image) and taking out the energy holding the blocks to by pulling them off the framework

Remember it took energy to push the block into the framework

THEN you can say the cube has lost energy

It will take a energy input to reassemble the cube

If you are plugging the blocks back onto the framework YOU are undergoing entropy loosing your energy which you will replace with the food you eat (your energy input pinched from the energy bound in the food being released into your body)

Talking of this

Coffee time

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No, it doesn't. Entropy depends on what you define.

That would be because you've defined some objects that can have different amounts of energy.

I think you're talking there about a change in entropy, objects don't have entropy. Entropy isn't a process either.

Taking a Rubik's cube apart will mean using energy (you have to do some work), whether you say the state it's in has more entropy or less, will depend on what you've defined. Note it's the state, not the cube or parts of it that you assign the entropy to. A gas at equilibrium has (a) maximum entropy (state).

Thermodynamic entropy is is something that can't be known (so trivially isn't known) about a particular state, equilibrium, defined in terms of energy. That doesn't mean entropy is always defined that way.

 

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I think I follow the following explanation

https://en.m.wikipedia.org/wiki/Introduction_to_entropy

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That explanation you think you follow has this to say:

"Classical thermodynamics is a physical theory which describes a "system" in terms of the thermodynamic variables of the system or its parts."

Which is to say, thermodynamic systems are defined (bounded) by thermodynamic variables. Energy is one of the variables.
But Claude Shannon showed that entropy doesn't have to be thermodynamically defined. We all have to live with it.

In fact, entropy is defined once you define informational boundaries--what can be known vs what cannot, in the system.
That thermodynamic entropy has units of Joules per degree Kelvin is just because the information has to be compatible. But actually dividing Joules by degrees Kelvin leaves what? Where are the physical units?