Evidence library
The evidence the formula rests on
Every source below is genuine, independently peer-reviewed work, each linked to its DOI and mapped to the term of P(t) it supports — from the discovery that neutrinos oscillate and carry mass, through the coherent enhancement of their cross-section, to graphene transport and the thermodynamics of non-equilibrium systems.
33peer-reviewed sources
1824–2022span of the literature
5research areas
23carry a resolvable DOI
How to read this library. These are established, independently peer-reviewed results. They set out the physics the framework rests on; the interpretation that ties them to a specific application is the model, not the papers. We deliberately do not sum citation counts — a highly-cited general review does not, by itself, validate any particular device.
- Freedman, D. Z. (1974). Coherent effects of a weak neutral current. Physical Review D 9, 1389. First prediction of coherent elastic neutrino–nucleus scattering (CEνNS). doi:10.1103/PhysRevD.9.1389
- COHERENT Collaboration (Akimov, D. et al.) (2017). Observation of coherent elastic neutrino–nucleus scattering. Science 357, 1123–1126. First experimental confirmation of CEνNS, above six sigma. doi:10.1126/science.aao0990 Deep dive →
- COHERENT Collaboration (Akimov, D. et al.) (2021). First measurement of coherent elastic neutrino–nucleus scattering on argon. Physical Review Letters 126, 012002. Independent confirmation of CEνNS on a second target nucleus. doi:10.1103/PhysRevLett.126.012002
- Super-Kamiokande Collaboration (Fukuda, Y. et al.) (1998). Evidence for oscillation of atmospheric neutrinos. Physical Review Letters 81, 1562–1567. First compelling evidence that neutrinos oscillate and therefore have mass. doi:10.1103/PhysRevLett.81.1562 Deep dive →
- SNO Collaboration (Ahmad, Q. R. et al.) (2002). Direct evidence for neutrino flavor transformation from neutral-current interactions. Physical Review Letters 89, 011301. Measured the total solar-neutrino flux across all flavours, confirming the solar model. doi:10.1103/PhysRevLett.89.011301 Deep dive →
- Kajita, T. (2016). Nobel Lecture: discovery of atmospheric neutrino oscillations. Reviews of Modern Physics 88, 030501. Nobel laureate's own account of the atmospheric-oscillation discovery. doi:10.1103/RevModPhys.88.030501
- McDonald, A. B. (2016). Nobel Lecture: the Sudbury Neutrino Observatory — observation of flavor change for solar neutrinos. Reviews of Modern Physics 88, 030502. Companion Nobel lecture on the solar-neutrino flavour-change result. doi:10.1103/RevModPhys.88.030502
- NOvA Collaboration (Acero, M. A. et al.) (2022). Improved measurement of neutrino oscillation parameters by the NOvA experiment. Physical Review D 106, 032004. A recent long-baseline measurement refining the oscillation parameters. doi:10.1103/PhysRevD.106.032004
- Nobel Committee for Physics (2015). Scientific background: neutrino oscillations. Royal Swedish Academy of Sciences. Establishes neutrino mass via oscillation — part of the framework's lineage. link ↗
- Particle Data Group (Workman, R. L. et al.) (2022). Review of Particle Physics (cosmic-ray muon flux). Progress of Theoretical and Experimental Physics 2022, 083C01. Reference values for one of the ambient input channels. doi:10.1093/ptep/ptac097
- Formaggio, J. A. & Zeller, G. P. (2012). From eV to EeV: neutrino cross sections across energy scales. Reviews of Modern Physics 84, 1307. The standard review of measured neutrino cross-sections over all energies. doi:10.1103/RevModPhys.84.1307
- Scholberg, K. (2006). Prospects for measuring coherent elastic neutrino–nucleus scattering at a stopped-pion source. Physical Review D 73, 033005. Framed the experimental route later realised by COHERENT. doi:10.1103/PhysRevD.73.033005
- Sakurai, J. J. (1994). Modern Quantum Mechanics (rev. ed.). Addison-Wesley. Scattering amplitudes, partial waves and the optical theorem behind σ(E).
- Mott, N. F. & Massey, H. S. W. (1965). The Theory of Atomic Collisions (3rd ed.). Oxford University Press. Foundational treatment of cross-sections and their energy dependence.
- Thibado, P. M. et al. (2020). Fluctuation-induced current from freestanding graphene. Physical Review E 102, 042101. Continuous measurable current from driven lattice motion in a loaded circuit. doi:10.1103/PhysRevE.102.042101 Deep dive →
- Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. (2009). The electronic properties of graphene. Reviews of Modern Physics 81, 109–162. The definitive review of graphene's Dirac-fermion electronics and phonon transport. doi:10.1103/RevModPhys.81.109 Deep dive →
- Bolotin, K. I. et al. (2008). Ultrahigh electron mobility in suspended graphene. Solid State Communications 146, 351–355. Shows how clean, suspended graphene reaches exceptional carrier transport. doi:10.1016/j.ssc.2008.02.024
- Grigorenko, A. N., Polini, M. & Novoselov, K. S. (2012). Graphene plasmonics. Nature Photonics 6, 749–758. How graphene couples to electromagnetic fields — relevant to the coupling term. doi:10.1038/nphoton.2012.262
- Giustino, F. (2017). Electron–phonon interactions from first principles. Reviews of Modern Physics 89, 015003. The rigorous framework linking lattice vibrations to charge transport (v_ph, Δp). doi:10.1103/RevModPhys.89.015003
- McIver, J. W. et al. (2012). Control over topological insulator photocurrents with light polarization. Nature Nanotechnology 7, 96–100. A directed photocurrent generated by symmetry control — an analogue of rectification. doi:10.1038/nnano.2011.214
- Ashcroft, N. W. & Mermin, N. D. (1976). Solid State Physics. Holt, Rinehart and Winston. Standard text on lattice vibrations, phonon dispersion and sound velocity.
- Ziman, J. M. (1960). Electrons and Phonons: The Theory of Transport Phenomena in Solids. Oxford University Press. Classic account of phonon transport underwriting the factor v_ph.
- Onsager, L. (1931). Reciprocal relations in irreversible processes, I. Physical Review 37, 405. Symmetry relations governing coupled irreversible flows. doi:10.1103/PhysRev.37.405
- Onsager, L. (1931). Reciprocal relations in irreversible processes, II. Physical Review 38, 2265. Continuation of the reciprocal-relations framework. doi:10.1103/PhysRev.38.2265
- Callen, H. B. & Welton, T. A. (1951). Irreversibility and generalized noise. Physical Review 83, 34. The fluctuation–dissipation theorem; bounds what equilibrium noise can do. doi:10.1103/PhysRev.83.34
- Reimann, P. (2002). Brownian motors: noisy transport far from thermal equilibrium. Physics Reports 361, 57–265. How broken symmetry rectifies unbiased fluctuations into directed transport. doi:10.1016/S0370-1573(01)00081-3
- Astumian, R. D. (1997). Thermodynamics and kinetics of a Brownian motor. Science 276, 917–922. Stochastic rectification in asymmetric, driven systems. doi:10.1126/science.276.5314.917
- Prigogine, I. (1977). Nobel Lecture: time, structure and fluctuations. Royal Swedish Academy of Sciences. Thermodynamics of dissipative structures in open, driven systems. link ↗
- de Groot, S. R. & Mazur, P. (1962). Non-Equilibrium Thermodynamics. North-Holland. Fluxes, forces and entropy production in continuous open systems.
- van Kampen, N. G. (2007). Stochastic Processes in Physics and Chemistry (3rd ed.). Elsevier. Master-equation treatment of directed transport and symmetry breaking.
- Feynman, R. P., Leighton, R. B. & Sands, M. (1963). The Feynman Lectures on Physics, Vol. I, Ch. 46 (Ratchet and Pawl). Addison-Wesley. A ratchet at equilibrium extracts no work; directed motion needs non-equilibrium. link ↗
- Carnot, S. (1824). Réflexions sur la puissance motrice du feu. Bachelier, Paris. Origin of the maximum efficiency of a heat engine — the archetypal bound.
- Shockley, W. & Queisser, H. J. (1961). Detailed balance limit of efficiency of p–n junction solar cells. Journal of Applied Physics 32, 510. The detailed-balance efficiency ceiling — the principal comparison case. doi:10.1063/1.1736034
Several results here are Nobel-recognised: neutrino oscillation (2015), graphene (2010), and the thermodynamics of irreversible processes (1968 and 1977).
Every entry links to its DOI. The same records, formatted for reference managers, are on the references page.