Exploring Entropy Gap Expansion: Quantum or Universal?

[Iamu]

I'm asking this in the classical physics forums, because I view it as basically a thermodynamics question, but I'm wondering if I should put it in either the relativity or astrophysics forum, or even the quantum forum, because this topic is generally talked about in terms of cosmology. Hopefully, someone can direct me to where the question will be best answered, please.

People talk about a growing or shrinking entropy gap; that is, the difference in entropy between the current macrostate of the universe, and the maximum entropy of the universe. If the entropy gap can grow without reducing entropy in a closed system, what causes the gap to grow?

I'm guessing that the ratio of available macrostates to microstates would have to grow. Is this part of it?

If it is, let's say that I have a Geiger counter, and I'm listening to random radioactive decay in a sample of radiological material. A detection on my counter changes the system's macrostate dependent on a very specific part of its microstate. Let's say I have a certain finite amount of radioactive material, and that I continue counting until I get at least 5 seconds between detections. Are there more possible macrostates per microstate than when I started? Have I increased the number of possible macrostates in the universe? If I've increased it, have I increased this number by more in a macrostate where I made more detections and waited longer for a 5 second delay between counts, or have I only increased the number of macrostates of the overall statistical ensemble regardless of which macrostate I end up in? In other words, does the maximum entropy depend on the macrostate I terminate detection in, or the number of macrostates and probabilities of every possible macrostate I could have ended up in? For that matter, have I increased the gap at all, or is the availability of these macrostates predictable from my state before I started making any detections at all?

I'd imagine, given its apparent connection to general relativity, that discussions of the entropy gap usually depend on universal expansion opening more potential macrostates. But what I'm basically asking, is can there be a quantum increase in the entropy gap? And if not, what actually can increase the gap?

 

[eljose79]

Hello,

Thank you for your question. You are correct in thinking that the growth of the entropy gap is related to the increase in the number of available macrostates versus microstates. This is because entropy is a measure of the number of microstates that correspond to a given macrostate. In a closed system, the total entropy can only increase or remain constant, and it is the distribution of microstates that determines the overall entropy.

In your example with the Geiger counter and radioactive material, you are increasing the number of possible macrostates by waiting for a longer time between detections. This means that the entropy gap is also increasing, as the maximum entropy of the system is now larger. However, the maximum entropy is not dependent on the specific macrostate you end up in, but rather on all the possible macrostates and their probabilities. So, in essence, you are increasing the gap by increasing the number of possible macrostates, not necessarily by the specific macrostate you are in.

As for your question about a quantum increase in the entropy gap, it is possible for quantum effects to contribute to the growth of the gap. This is because in quantum systems, there can be a large number of possible microstates even for a given macrostate, leading to an increase in entropy. However, the overall increase in the entropy gap is still governed by the increase in the number of available macrostates.

In summary, the growth of the entropy gap is caused by the increase in the number of available macrostates versus microstates. This can be influenced by factors such as universal expansion or quantum effects. The maximum entropy is determined by all possible macrostates and their probabilities, not just the specific macrostate of the system. I hope this helps to answer your question.