Technology

Schubart–NEG Master Equation

Holger Thorsten Schubart 2024

P(t) = ∫ Φ(E,θ,t) · σ(E) · Δp · v_ph · η_conv dE dθ

What It Means

The Schubart–NEG Master Equation describes a fundamentally new approach to energy harvesting. Rather than relying on visible light like solar panels or chemical reactions like batteries, this equation formalizes how invisible radiation — including neutrinos, cosmic muons, ambient electromagnetic fields, and thermal fluctuations — can be converted into usable electrical power through engineered nanostructures.

In its canonical form the equation states that the electrical power output P(t) is the integral, over incident energy E and incidence angle θ, of five coupled physical factors: how much ambient flux arrives, Φ(E,θ,t); how strongly that flux couples to the medium, σ(E); how much momentum each interaction delivers, Δp; how fast the resulting disturbance travels through the lattice, the phonon velocity v_ph; and what fraction of the captured energy is finally rectified into directed current, η_conv. Written this way, each mechanism appears as a separate, individually engineerable term.

The Neutrino Energy Group also states the relation in a compact, device-oriented form that folds the microscopic transport factors Δp and v_ph into an effective coupling σ_eff and a single device efficiency η, and replaces the angular integral with an integral over the active converter volume:

P(t) = η · ∫_V Φ_eff(r,t) · σ_eff(E) dV

The two statements are equivalent. The group's published reference treats the five-factor form as canonical, because it exposes each physical mechanism separately, and describes the compact volume form as the convenient device-level summary. A long-term-mean version, ⟨P⟩ = η · ∫_V ∫ Φ_eff(E,r) · σ_eff(E) dE dV, integrates additionally over energy.

One further point is worth drawing out, because it is easy to miss: the canonical equation is written technology-neutrally. Φ is any ambient radiation field, σ is any coupling mechanism, and the medium enters only through v_ph and η_conv. On that reading it is a general relation for continuous ambient energy conversion in open systems, and neutrinovoltaics — where Φ is the neutrino and ambient-radiation flux and the medium is a multilayer graphene–silicon nanomaterial — is one application of it rather than the whole of it.

What makes this equation distinctive in the landscape of energy physics is that it treats the energy environment as a composite field. The universe is permeated by particles and radiation at every scale — from the 60 billion neutrinos passing through every square centimeter of Earth's surface every second, to the cosmic microwave background, to the ambient electromagnetic fields generated by modern infrastructure. The Schubart–NEG equation provides the mathematical framework for harvesting energy from this omnipresent but previously untapped flux.

The Variables

Symbol	Meaning	Unit
P(t)	Instantaneous electrical power output as a function of time — the quantity the framework predicts	Watts (W)
Φ(E,θ,t)	Radiation flux density — ambient radiation arriving per unit area, energy, solid angle and time. Technology-neutral: any ambient field. In the neutrinovoltaic case, the composite environment of solar and cosmic neutrinos, atmospheric muons, ambient RF/microwave fields and thermal background	per m²·eV·sr·s
σ(E)	Interaction (coupling) cross-section — how strongly the incoming field couples to the absorbing medium at energy E	m² or barn
Δp	Momentum transfer delivered to the medium per interaction — the impulse that seeds transport	kg·m/s
v_ph	Characteristic transport (phonon) velocity of the medium — how fast the disturbance propagates toward usable motion. In the neutrinovoltaic case, graphene's phonon velocity	m/s
η_conv	Conversion efficiency — the fraction of captured energy rectified into directed electrical output	Dimensionless
E, θ	Integration variables — incident energy and incidence angle, integrated across the full spectrum and angular acceptance	eV, radians
In the compact device-oriented form
η	Total device efficiency — a dimensionless factor between 0 and 1 that absorbs η_conv and the transport terms	Dimensionless
Φ_eff(r,t)	Effective external momentum-flux density at each point of the active material	W/m² or eV/(cm²·s)
σ_eff(E)	Structural coupling coefficient — bundles Δp and v_ph together with device geometry, material composition, impedance matching and resonance selectivity of the multilayer graphene–silicon nanocomposite	m² or barn-equivalent
V	Active material volume over which the integration is performed	m³
r	Position vector within the active material	m
t	Time	s

Historical Context

The equation was developed by Holger Thorsten Schubart and the Neutrino Energy Group (NEG) as a theoretical foundation for neutrinovoltaic technology. Unlike many breakthroughs in energy physics where the technology preceded the theory, the Schubart–NEG equation was formulated as a predictive framework — the mathematics came before the machine.

The development builds on several key scientific milestones. The 2015 Nobel Prize in Physics, awarded to Takaaki Kajita and Arthur B. McDonald for demonstrating that neutrinos have mass, confirmed that these particles carry kinetic energy and can therefore, in principle, interact with matter in ways that transfer energy. The subsequent advances in graphene physics — particularly the discovery that multilayer graphene exhibits unique vibrational properties when exposed to external radiation — provided the material science foundation. Schubart's contribution was to synthesize these separate scientific threads into a single, unified equation that governs the energy conversion process.

The Physics Behind It

The equation rests on well-established physics. Neutrinos, despite their weak interaction cross-section, carry momentum. When passing through a carefully engineered multilayer structure of doped graphene and silicon, they can induce atomic-scale vibrations. These vibrations, combined with those generated by other ambient radiation sources, create a coherent mechanical response in the nanostructure that can be converted to electrical current through the piezoelectric-like properties of the composite material.

The coupling coefficient σ_eff is the critical engineering parameter. It encapsulates decades of materials science — the precise layering of graphene sheets, the doping profiles, the resonance tuning of the nanostructure to maximize energy absorption across a broad spectrum of incident particle energies. The Neutrino Energy Group employs artificial intelligence models to optimize this parameter, simulating how atomic vibrations evolve under different flux conditions to continuously improve conversion efficiency.

Why It Matters

The Schubart–NEG equation represents a paradigm shift in how we think about energy. Unlike solar or wind energy, the radiation described by Φ_eff is available 24 hours a day, in any weather, through walls and underground. If the coupling coefficient σ_eff can be engineered to sufficient levels — which is the active frontier of neutrinovoltaic research — this equation describes a technology that could provide continuous, decentralized power anywhere on Earth without fuel, emissions, or dependence on weather conditions.

Where It Sits Among Governing Relations

The group's published reference places the equation deliberately: every mode of energy conversion is anchored by one governing relation, and the claim is that this one occupies that position for continuous ambient conversion. Heat engines have the Carnot bound, which fixes the ceiling efficiency between two temperatures regardless of construction. Single-junction solar cells have the Shockley–Queisser limit, which uses detailed balance to fix maximum efficiency from the incoming photon flux and unavoidable radiative losses.

Three structural differences are claimed. The driving input is continuous and omnidirectional rather than intermittent and directional, so availability does not stop at nightfall. The output is a time-resolved power curve P(t) rather than a single efficiency ceiling, because the flux carries an explicit time argument. And the design lever is the coupling σ and efficiency η of an engineered medium, raised through nanostructuring, rather than band-gap selection.

The comparison is worth taking seriously as a statement about structure, and worth reading precisely. Carnot and Shockley–Queisser are established textbook relations that set upper bounds — they tell you what is impossible. The Schubart Master Formula is a published framework that computes an output from assumed inputs, which is a different kind of claim, and one whose full-scale net output the Neutrino Energy Group itself describes as awaiting independent validation. Our longer treatment of the comparison is in the Shockley–Queisser limit and the governing relations of energy.

Applications

The Neutrino Power Cube — A fuel-free power generation system producing 5-6 kW of continuous net electrical output, designed for residential use and currently in pilot testing.
The Pi Car Project — An electric vehicle concept powered by neutrinovoltaic cells integrated into the body, supplementing battery range with continuous energy harvesting from ambient radiation.
Off-grid and disaster relief power — Because the energy flux is omnipresent, neutrinovoltaic devices could provide emergency power in locations where solar, wind, and grid infrastructure are unavailable.
IoT and remote sensors — Low-power devices in inaccessible locations could be powered indefinitely without battery replacement.
Deep space and submarine applications — Where solar energy is unavailable, the neutrino flux remains constant, offering a potential power source for deep-sea and interplanetary missions.

Scientific Foundation

The theoretical framework of this equation is supported by 15 peer-reviewed publications with over 36,000 combined citations from journals including Physical Review Letters, Science, Nature Nanotechnology, and Reviews of Modern Physics.

View the complete scientific foundation →