The Vacuum Fluctuation Theorem: Exact Schroedinger Equation via Nonequilibrium Thermodynamics

By assuming that a particle of energy hbar.omega is actually a dissipative system maintained in a nonequilibrium steady state by a constant throughput of energy (heat flow), the exact Schroedinger equation is derived, both for conservative and nonconservative systems. Thereby, only universal properties of oscillators and nonequilibrium thermostatting are used, such that a maximal model independence of the hypothesised sub-quantum physics is guaranteed. It is claimed that this represents the shortest derivation of the Schroedinger equation from (modern) classical physics in the literature, and the only exact one, too. Moreover, a “vacuum fluctuation theorem” is presented, with particular emphasis on possible applications for a better understanding of quantum mechanical nonlocal effects.

💡 Research Summary

The paper proposes a novel derivation of the Schrödinger equation grounded in modern nonequilibrium thermodynamics. The author starts by modeling a quantum particle as a classical harmonic oscillator of energy ℏω that is not isolated but continuously driven by a heat flow from the vacuum. This heat flow maintains the oscillator in a nonequilibrium steady state (NESS), a concept borrowed from stochastic thermodynamics and the fluctuation theorem. By assuming that the vacuum acts as an infinite thermal reservoir providing a constant throughput of energy, the author introduces an effective temperature T_eff and relates the entropy production σ to the heat current Q̇ via σ = Q̇/T_eff.

From the NESS condition, the continuity equation for the probability density ρ(x,t) and a Hamilton‑Jacobi‑like equation for the phase S(x,t) are derived. The heat current appears as an additional term in the phase equation, effectively generating the quantum potential Q that is normally introduced ad hoc in the Madelung formulation. By defining the complex wavefunction ψ = √ρ exp(iS/ℏ), the two equations combine into the familiar time‑dependent Schrödinger equation iℏ∂_tψ =