Thank you very much, Jake!!!! You’re awesome.

Thank you for the very kind words, Jake!!!

Very beautiful results, Nelly! Already started my late morning reading it 😍

My happiest memories are tied to this university, this office, and that chapter of my life. Even cooler to see my old office mate getting his PhD tomorrow! Finally get to use this picture (taken in 2021, just sitting in my gallery waiting for this moment):

Entangled exit strategies

Hmm… The only quantum aspect is assuming a closed system evolving under energy-preserving unitaries. This leads to a partial order on state transformations. Replacing unitaries with Gibbs-preserving stochastic matrices gives the same result-nothing uniquely quantum. But maybe I’m missing the point.

Sorry for not being clearer - I’m in a shelter at the top of a mountain in Japan right now. Hard to type and be coherent haha

I was referring to the first one showing the partial order for classical states (diagonal in the energy eigenbasis): „Nat. Commun. 4, 2059 (2013)”.

For the cones: „Phys. Rev. E 106, 064109 (2022)”.

But yes, Kamil & Matteo also showed this for Markovian thermal processes…

In the video you can see the set of achievable states under thermodynamic transformations for a given an out of equilibrium state (4D state) in contact with a bath: green is the achievable states, blue the set that I achieve the initial state and red the set of incomparable states….

This was formally proven a few years ago! The set of states achievable under thermodynamic transformation follows a partial-order relation called “thermomajorisation”. This is a beautiful result that illustrates your point.

That’s amazing Shintaro! Congrats.

Here’s the app: coffeeadastra.com/2019/04/07/a...

His blog is great too!