It begs the question : how much information is there in a drop of water ?
Does the algorithm has to simulate every one of the water molecules, or can it adaptively only needs to preserve the macroscopic quantities while preserving the consistency of the microscopic level (aka information conservation).
Most physical phenomenons exhibit some degree of self synchronization, and self similarity, witness of some kind of information redundancy. It happens at all scales of the universe, from particles which self-organize into crystals, spinning rocks coalescing into planets, stars forming black-holes to store information on their surface instead of the volume.
All these physics rules allow huge speed-up in computation, because once a quantity doesn't change, a billion years for a billion stars can go in an instant.
Information is conserved, but information wants to diffuse. That is the cosmic entropic battle which life is fighting.
Life are the computations which can't be shortcutted.
I was watching a documentary and I heard about the problem of information does not disappear in the universe. What does this mean. I have a feeling that information in quantum physics has a different meaning but I don’t understand what it is.
(You can look at the technical concepts of "Fisher Information" and "conservation of probability", if you want more details for the quantum case)
It's then about, what you want to describe.
In quantum physics you want to describe the full state. In our world you want to describe statistics about the full state we have access to : the "observables".
Among those statistics there are some quantities which are expected to be conserved and easily accessible. In our day to day language information is about the value of these quantities, and the number of bits necessary to describe these values, which is a lower bound of the full state uncompressed information.
When we have the full state, the rules of evolution are reversible therefore you cannot lose information, if you know the full state at any one time, you can know it at any other time in the future or past, it's just a matter of computation to time-evolve the system.
What gets fun is that information can get compressed. Imagine dropping a piece of glass to the floor and it shatters.
Before the shattering it can easily be described as a uniform square of glass, but after, you have to describe the positions of every pieces. But because the system is deterministic there is the same information before and after : you can describe it simply by stating it's the time-evolution of uniform square of glass at time post-shattering.
But if you want to do some computation on it, you can't always work in compressed form. You then need to find a suitable representation which allows to perform the computation you need efficiently.
How much will need to be materialized will depend of the rules of your system.
A frequency so slow that the billions of years elapsed since the creation of the universe, used negligible computation power compared to the resources needed for a single second one century later when the simulation had to be halted having exhausted all computational credits.