Asymmetric relaxations through the lens of information geometry

Abstract 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.