Representing Measurement as a Thermodynamic Symmetry Breaking

Abstract

Descriptions of measurement typically neglect the observations required to identify the apparatus employed to either prepare or register the final state of the “system of interest.” Here, we employ category-theoretic methods, particularly the theory of classifiers, to characterize the full interaction between observer and world in terms of information and resource flows. Allocating a subset of the received bits to system identification imposes two separability constraints and hence breaks two symmetries: first, between observational outcomes held constant and those allowed to vary; and, second, between observational outcomes regarded as “informative” and those relegated to purely thermodynamic functions of free-energy acquisition and waste heat dissipation. We show that breaking these symmetries induces decoherence, contextuality, and measurement-associated disturbance of the system of interest.