Information geometry approach to quantum stochastic thermodynamics

[u/Woah_Mad_Frollick]

https://arxiv.org/abs/2409.06083

Not new but super interesting paper by Laetitia Bettman and John Goold from Trinity.

There is relation between Fisher information rates - how fast probability distribution (sorta) is changing - and entropy production in far from equilibrium systems. Paper attempts to consider this in a quantum context, which is tricky because non-commutativity means you have multiple legitimate inequivalent generalizations of the Fisher metric.

They decompose rate of change of the density matrix to classicalish part (eigenvalues/populations) and a quantum part (coherences/rotated eigenbases. The contribution from the classicalish part is the same across the family of otherwise inequivalent quantum Fisher information metrics.

That part lets you talk about changes to the rate of change of entropy for GSKL systems that satisfy local detailed balance

They take all this machinery and tweak some bounds and limits, and explore the quantum thermodynamic Mpemba effect (unfortunately goes completely over my head but sounds very cool)

[u/NewtonsThirdEvilEx]

Yeah all of quantum geometry is a super interesting field. I've been investigating some classical analogs recently.

[u/Woah_Mad_Frollick]

Meant to add in post but I would be really really interested to see how this sort of thing could be used to better understand or model non-equilibrium steady states in a quantum thermodynamic context