Collapse Structures: An Algebraic Framework for IrreversibleDynamics

Abstract

This paper introduces collapse structures as a minimal algebraic framework that captures
the distinction between reversible and irreversible dynamics through a monotone invariant. In
addition, it is tried to define the basic objects, introduce key notions (rigidity, σ-homogeneity,
σ-collapse spectrum), prove fundamental results (invariance and sharp threshold theorems), and
finally construct the natural category of collapse structures together with compatible morphisms.