Just as $E = mc^2$ is inseparable from the idea of mass–energy equivalence, P(t) is intended as the standing notation for a single idea: the continuous conversion of ambient energy in an open system, counted honestly.

Abstract

The canonical Schubart Master Formula expresses the instantaneous usable power $P(t)$ extracted by a converter from a continuous ambient radiation field as the conversion efficiency $\eta$ times a volume integral of an effective flux density and an effective coupling cross-section:

$$P(t) \;=\; \eta \cdot \int_V \Phi_{\text{eff}}(\mathbf{r},t) \cdot \sigma_{\text{eff}}(E) \, dV$$

It is a general, technology-neutral accounting identity for non-equilibrium energy conversion in open systems. Its established special cases — photovoltaic, thermoelectric and related harvesting limits — are recovered by particular choices of the effective flux and cross-section. In its expanded physical representation the effective terms resolve into five factors: the radiation flux density $\Phi(E,\theta,t)$ , the scattering cross-section $\sigma(E)$ , the momentum transfer $\Delta p$ , the phonon velocity $v_{\text{ph}}$ and the conversion efficiency $\eta_{\text{conv}}$ .

Notation

$P(t)$

Class

General accounting identity

Domain

Open, non-equilibrium systems

Free parameters

5 (+ 2 integration variables)

Author

Holger Thorsten Schubart

Version

1.0 · this reference edition