Entropy change in a boiling egg

I’ve come across several claims that a (hard) boiled egg has greater entropy than an unboiled egg. None of them cite any peer-reviewed research to back up their claim. While it is possible that entropy increases when you boil an egg, it is also possible that it does not. It is even possible that it stays the same.

I did my own literature search to see if I could find any publication that answered the question. What I found left the question very much up in the air. So I contacted Greg Weiss, a scientist who has done research on a related topic: ‘unboiling’ an egg: https://www.livescience.com/49610-scientists-unboil-egg.html . Dr. Weiss was kind enough to discuss the topic with me via email.

Here’s the tl;dr summary: Whether a hard-boiled egg has greater entropy all boils down to the question of how structured are the assemblies found in aggregated ovalbumin. Furthermore, we can't just consider the assemblies found in the ovalbumin aggregate since we're talking about assemblies composed of all the types of protein in the overall albumen. (BTW, it's important to note that heated egg white doesn't just form any type of aggregate, it forms a gel, which presumably implies additional structure.)

For those who are interested in the details, here is the full email thread: https://docs.google.com/document/d/1Yt-usFLd3sm7MYpVTfwy3Yza6t3Ub6Q3lUZo7on5_wk/edit?usp=sharing

An intuitive way of thinking about boiling an egg, is that you start a pool with a bunch of balls of yarn floating in it. Then when you heat the egg, it causes all the balls of yarn to unravel, and rather than a pool with some balls in it now it's a tangled mess of yarn. Before, each ball was free to move around as a unit, now each segment of each strand can wiggle around separately. This creates a whole lot more possible states and increases the entropy.

If you do an entropy balance on an egg as a closed system (Make it closed by sealing it if you have to), it looks like this: $$\frac Q{T_b} + \sigma = S_{\rm final} - S_{\rm initial}$$ where $T_b$ is the absolute temperature of the egg and sigma is the entropy production. Then adding heat to this system produces a positive $Q\over T_b$ entropy transport term into the egg. The entropy production (sigma) of this (or any) process is always positive, so the entropy of the egg increases as it is boiled and hardens. That is, of course, unless the egg gives off heat as it hardens. Then, if sigma is small enough, the egg's entropy could decrease. So it depends on whether or not the egg hardening process is endothermic or exothermic.