Author: Nova Spivack
Date: June 2025
Abstract
The fundamental energy-complexity relationship dE = α₀dΩ (where α₀ = πkᵦT) from IP.Found establishes that information geometric complexity has direct energetic consequences. This paper develops the rigorous classical field theory for spatially distributed complexity by: (1) defining the complexity density field ω(x,t) with dimensions [L⁻³] as the fundamental dynamic variable representing dimensionless information complexity per unit volume, (2) constructing the thermodynamically consistent Lagrangian L = ½κ(∂ψ)² – ½β²ψ² (for fluctuations ψ around a thermal equilibrium ω₀), which directly implements the energy-complexity relationship through the underlying potential V(ω) = πkᵦTω + ½β²ω², and (3) analyzing the resulting field dynamics and gravitational effects.… Read More “The Ω-Field: Classical Field Theory for Information Geometric Complexity”