Asymmetric relaxations through the lens of information geometry

We frame Newton's law of cooling as a gradient flow within the context of information geometry. This connects it to a thermodynamic uncertainty relation and the Horse-Carrot theorem, and reveals novel instances of asymmetric relaxations in endoreversible processes. We present a general criterion for predicting asymmetries using the Amari-Chentsov tensor, applicable to classical and quantum thermodynamics. Examples include faster cooling of quantum ideal gases and relaxations that resemble the Mpemba effect in classical ideal gases.