There’s a weird geometric reason why it’s actually way faster to heat something up than it is to cool it back down.
April 2, 2026
Original Paper
Gradient systems and asymmetric relaxations in view of Riemannian geometry
arXiv · 2604.00192
The Takeaway
By studying the curved 'geometry' of all possible states a system can occupy, scientists found a universal asymmetry: systems return to a hot state more quickly than they relax to a cold one. This explains a long-observed thermal behavior by showing that the path to higher energy is mathematically 'shorter' or more direct than the path to cooling.
From the abstract
In dually flat manifolds, there is a deep connection between gradient flows and pregeodesics. This was one of the many important contributions of Amari to information geometry. In this paper, we extend the study of this relationship to general Riemannian manifolds. Our result does not impose conditions of flatness on the connection or symmetry on its non-metricity tensor, thus broadening the geometric setting beyond Hessian manifolds. Within this framework, we provide a criterion for comparing r