A Categorical Approach to Statistical Mechanics

Grégoire Sergeant-Perthuis

Abstract: Rigorous’ Statistical Mechanics is centered on the mathematical study of statistical systems. In this article, we show that important concepts in this field have a natural expression in terms of category theory. We show that statistical systems are particular representations of partially ordered sets (posets) and express their phases as invariants of these representations. This work opens the way to the use of homological algebra to compute phases of statistical systems. In particular we compute the invariants of projective poset representations. We remark that in this formalism finite-size systems are allowed to have several phases.

External IDs:dblp:conf/gsi/SergeantPerthuis23