Add general entropy functionality to EOS

[jhp-lanl]

PR Summary

This MR adds the basic entropy hookups for entropy lookup functions to be exposed in the general EOS type.

There are five main changes in this effort:

1. Add entropy lookups to the Variant class. This basically forces the EOS API to now provide entropy lookups so it needs to be implemented in some form everywhere.
2. Add a default function to raise an error that entropy isn't implemented and have the entropy functions call this function by default.
3. Use the ideal gas EOS as a prototype for adding entropy to other EOS. The functional form is fairly
4. Incorporate entropy into the modifiers correctly. I could have just used the error functionality, but it was actually fairly easy since most modifiers won't modify the entropy. I had to prove to myself how entropy should be modified with scaling ratios, but I think it's the correct approach.
5. Add a lot of documentation about entropy and complete vs incomplete EOS.

I wanted to implement entropy for at least one analytic EOS in this MR because I think it exposes important implications for other analytic EOS. Specifically, it demonstrates that the entropy is divergent at zero temperature for EOS with constant heat capacity, which further emphasizes the importance of the reference state in the entropy calculation.

There are a lot of changes to the documentation where I wanted to add what I've learned in researching how to implement entropy. There are also some cosmetic changes that can be ignored (especially in the Vinet EOS) that just
made things easier for me to read in text form.

To do:

• Create a test for the ideal gas entropy

First step on addressing #210

PR Checklist

• Adds a test for any bugs fixed. Adds tests for new features.
• Format your changes by using the make format command after configuring with cmake.
• Document any new features, update documentation for changes made.
• N/A Make sure the copyright notice on any files you modified is up to date.
• After creating a pull request, note it in the CHANGELOG.md file
• N/A If preparing for a new release, update the version in cmake.

[jhp-lanl]

@aematts can you review this?

Also @Yurlungur and @dholladay00 can you give things a brief look to make sure you agree with my strategy for defaulting EOS to throw errors?

[jhp-lanl]

I should add that I haven't built the code yet 😶 so there's probably lots of little issues I need to fix tomorrow. I just wanted to get this up so people could start looking at things.

[Yurlungur]

👍 This all seems reasonable to me.

[jhp-lanl]

This MR depends on #234

[jhp-lanl]

@aematts any thoughts?

@dholladay00 I don't think there's much for you to review, but make sure you agree with how I'm implementing the default entropy error throwing

[jhp-lanl]

@aematts any thoughts?

I should add, I'd greatly appreciate your eyes on the documentation, @aematts . I've written some stuff up about EOS theory that mirrors the document you wrote (which I cited). I'd love your feedback there if you can give it.

[Yurlungur]

This looks good. Thanks for doing this, @jhp-lanl ! A high priority should be enabling entropy in the tabulated EOS's but getting the framework in place is an important first step.

[aematts]

@aematts any thoughts?

I should add, I'd greatly appreciate your eyes on the documentation, @aematts . I've written some stuff up about EOS theory that mirrors the document you wrote (which I cited). I'd love your feedback there if you can give it.

I have been to a conference this week and have had no time to even read my emails. I will get to this sometime next week.

[jhp-lanl]

@aematts any thoughts?

I should add, I'd greatly appreciate your eyes on the documentation, @aematts . I've written some stuff up about EOS theory that mirrors the document you wrote (which I cited). I'd love your feedback there if you can give it.

I have been to a conference this week and have had no time to even read my emails. I will get to this sometime next week.

@aematts I'm going to delay until the end of the day Monday to merge this, but even if you don't have time to make comments by then, please feel free to make comments even after these changes are merged. It will then be fairly easy to just create a new PR to address your comments on these changes, especially if most of the comments are in the documentation.

Normally I'd just wait for all the feedback to come in, but given that this MR has been open for a while already without feedback and that Jonah has a student waiting for these changes, I figure it's possible to merge these changes with the expectation that more changes will be required down the road. Besides, I'll need to create another MR to add in EOSPAC, spiner, and Davis entropy capabilities.

[dholladay00]

@jhp-lanl what's the timeline for merging this?

[jhp-lanl]

@dholladay00 sorry last week was pretty crazy. I was going to merge it last week but forgot about it. I'll try to resolve the conflicts in the changelog this afternoon and get it merged.

@aematts feel free to give feedback after the MR has been merged and I can address your feedback in subsequent MRs

[jhp-lanl]

I'll try to resolve the conflicts in the changelog this afternoon and get it merged.

I'll make this a top priority for tomorrow

[jhp-lanl]

Merging... all CI is green