The Architectural Magnitude A Structural State Variable for Statistical Thermodynamics, Green Functions, and Physical Observables
Year: 2026
Type: preprint
Abstract: Statistical thermodynamics establishes a quantitative relationship between microscopic states and macroscopic observables through the partition function. In the conventional formulation, the primitive microscopic objects are particle configurations, spin configurations, or field configurations. The resulting statistical ensembles determine thermodynamic quantities such as internal energy, entropy, free energy, and heat capacity. Although this framework has been extraordinarily successful, the microscopic state space depends strongly on the particular physical system under consideration. No general structural state variable presently exists that characterizes microscopic organization independently of its specific physical realization. In this paper, we propose that architectures constitute a primitive class of microscopic objects. Every finite architecture admits a Canonical Architectural Decomposition into transport, interaction, holonomy, and recursion. Based on this decomposition, we introduce the Architectural Magnitude as a structural state variable that characterizes architectural complexity independently of its physical implementation. Architectural ensembles are then proposed as structural analogues of conventional statistical ensembles. Replacing microscopic configurations by architectures leads naturally to an architectural partition function from which thermodynamic quantities may be reconstructed. Within this framework, energy, entropy, free energy, and response functions become derived quantities associated with architectural ensembles rather than with individual particle configurations. The same structural framework further provides a natural setting for Green functions, operator reduction, and spectral observables. The present work establishes the mathematical foundations of architectural statistical mechanics. While the construction of architectural ensembles and the associated partition function are formulated mathematically, their interpretation as a universal microscopic description of physical systems is proposed as a hypothesis for further investigation.
Author: Arneth, Borros
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171217543