  We introduce a novel perspective on Newton's Law of Cooling by framing it
within the context of information geometry. By characterizing it as a specific
representation of a gradient flow, we establish a connection with the
well-known Horse-Carrot Theorem and reveal previously unexplored instances of
asymmetric relaxations in the context of endoreversible processes. We present a
completely general and practical criterion for predicting asymmetries based on
the Amari-Chentsov tensor, whose applicability extends to both classical and
quantum thermodynamics. Illustrative examples include faster cooling down of
quantum ideal gases, and relaxations reminiscent of the Mpemba effect in
classical ideal gases.
