I have no clue what you mean by approaching computation from the point of view of entropy, entropy is a measure of the degree of disorder in a system, how is that a method of performing computation?
The step function does not encode memory. The step function is a function that takes memory state 1 as input, and outputs memory state 2 as output. The step function itself doesn't change, it stores no information.
In physical terms, the step function is the CPU, minus the caches, registers and other modifiable state. Memory is the disk and ram and all the CPUs caches and registers. You can't tell me anything about what the input to the CPU is, or what it is actually doing (other than that it is capable of running arbitrary x64 assembly), without looking at the state.
A function does store information. The common definition of a function is the set (R,(X,Y)) where R is the graph of the function (consisting of the pairs) and X and Y are domain and codomain, respectively.
Computation can be seen as some act of carrying out logic. And in turn, logic can be approached via entropy. There are a lot of people working in QM, computation and entropy. But the simpler definition is just via partitions (and you especially don't have to insist on it being in the world of QM either). [1]
The selection of the function to use contains information. Once a function is given (e.g. the function specifying the x64 ISA), the function stores no information, it is immutable.
(Sorry about replying so late, I know it's unlikely you will see this, oh well)
