THEORETICAL FRAMEWORK
An AI that generates text consumes energy and maintains coherence, exactly like a brain thinking or a body walking.
This expenditure leaves a measurable trace, independent of the semantic content of the response.
Measuring coherence and effort at the same time means identifying the exact moment when the response reaches its maximum density.
Beyond that point, the system drifts: it wastes tokens, dilutes information, and increases the risk of error.
Before that point, the response is incomplete.
The right moment is measurable, in real time, token by token.
This measurement produces a signal.
This signal can be used to stop generation at the right time, restart it, or trigger human supervision.
NeoMundi’s measurement instrument provides the neutral measurement. AI providers and agent orchestrators retain decision-making authority.
Three direct consequences: energy sobriety (fewer unnecessary tokens), denser informational quality, reduction in the risk of hallucination and drift, and a gain in overall trust.
At a global scale, language model inference consumes massive amounts of water and electricity. Every token an AI does not produce unnecessarily is a cost avoided. A signal capable of saying “stop, you’re done” has a tangible climate impact.
This is sobriety in the literal sense.
The European AI Regulation (EU AI Act) requires traceability of model behavior in production for high-risk systems.
Real-time thermodynamic measurement directly addresses this requirement.
It is a physics of decision applied to machines that speak.
LAW E™
The E in Law E™ encompasses four dimensions:
- Energy: the thermodynamic expenditure underlying the production of each token.
- Economy: the principle of least effort, maximum information for minimum expenditure.
- Ethics: governance derived from measurement, traceability as a condition of accountability.
- Emergence: the collective properties that appear when the framework is applied to interacting agents.
One measurement (Energy), one principle (Economy), one consequence (Ethics), one horizon (Emergence).
SCIENTIFIC ANCHORING
Scientific Foundations
The framework is part of a precise lineage in the science of dynamic systems.
Dynamic Stability – Lyapunov, 1892
A system is stable if a well-chosen energy function decreases over time. Law E™ draws on this intuition to define a stability measure applicable to generative processes.
Active Inference – Friston, 2010
An intelligent system minimizes free energy, i.e., the gap between what it predicts and what it observes. The free energy principle frames the thermodynamic reading of generative cognition.
Self-Organization – Prigogine, 1977
Dissipative structures maintain their internal order at the cost of continuous energy expenditure. A language model in production is, in this respect, a dissipative structure.
Law E™ articulates these three lineages into a unified framework applicable to contemporary generative systems.
The hypothesis, its mathematical formulation, and its falsifiability conditions are published on Zenodo (DOI 10.5281/zenodo.19385052).
The measurement methodology derived from the framework is available on GitHub.