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This is not the same as: How many bytes can the observable universe store?

The Bekenstein bound tells us how many bits of data can be stored in a space. Using this value, we can determine the number of unique states this space can be in.

Imagine now, we are to simulate this space by enumerating each state along with which states it can transition to with a probability for each transition.

How much information is needed to encode the number of legal transitions and the probabilities? Does this question even make sense? If so, is there any indication that any of these probabilities are or are not Computable numbers?

Edit
Here's a thought experiment.

1. Select your piece of space and start recording all the different states you see.
2. If the Bekenstein bound tells us we can store n bits in our space, wait until you see 2^n different states. Now we've seen all the states our space can be in (otherwise we can violate the Bekenstein bound).
3. For any state, record any other state that the space can legally transition to without violating any physical laws.

To simulate this portion of space, take it's state and transition it to a legal state. Repeat.

We have only used a finite number of bits and we have modeled a section of space.

This is not the same as: How many bytes can the observable universe store?

The Bekenstein bound tells us how many bits of data can be stored in a space. Using this value, we can determine the number of unique states this space can be in.

Imagine now, we are to simulate this space by enumerating each state along with which states it can transition to with a probability for each transition.

How much information is needed to encode the number of legal transitions and the probabilities? Does this question even make sense? If so, is there any indication that any of these probabilities are or are not Computable numbers?

Edit
Here's a thought experiment.

1. Select your piece of space and start recording all the different states you see.
2. If the Bekenstein bound tells us we can store n bits in our space, wait until you see 2^n different states. Now we've seen all the states our space can be in (otherwise we can violate the Bekenstein bound).
3. For any state, record any other state that the space can legally transition to without violating any physical laws.

To simulate this portion of space, take it's state and transition it to a legal state. Repeat.

We have only used a finite number of bits and we have modeled a section of space.

This is not the same as: How many bytes can the observable universe store?

The Bekenstein bound tells us how many bits of data can be stored in a space. Using this value, we can determine the number of unique states this space can be in.

Imagine now, we are to simulate this space by enumerating each state along with which states it can transition to with a probability for each transition.

How much information is needed to encode the number of legal transitions and the probabilities? Does this question even make sense? If so, is there any indication that any of these probabilities are or are not Computable numbers?

This is not the same as: How many bytes can the observable universe store?

The Bekenstein bound tells us how many bits of data can be stored in a space. Using this value, we can determine the number of unique states this space can be in.

Imagine now, we are to simulate this space by enumerating each state along with which states it can transition to with a probability for each transition.

How much information is needed to encode the number of legal transitions and the probabilities? Does this question even make sense? If so, is there any indication that any of these probabilities are or are not Computable numbers?

Edit
Here's a thought experiment.

1. Select your piece of space and start recording all the different states you see.
2. If the Bekenstein bound tells us we can store n bits in our space, wait until you see 2^n different states. Now we've seen all the states our space can be in (otherwise we can violate the Bekenstein bound).
3. For any state, record any other state that the space can legally transition to without violating any physical laws.

To simulate this portion of space, take it's state and transition it to a legal state. Repeat.

We have only used a finite number of bits and we have modeled a section of space.