Entropy, Vol. 23, Pages 1371: Justifying Born`s Rule Pα = |Ψα|2 Using Deterministic Chaos, Decoherence, and the de Broglie-Bohm Quantum Theory (Entropy)

In this work, we derive Born`s rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to an environment made of “qubits” (i.e., Bohmian pointers), we show that entanglement together with deterministic chaos leads to a fast relaxation from any statistical distribution ρ(x) of finding a particle at point x to the Born probability law |Ψ(x)|2. Our model is discussed in the context of Boltzmann`s kinetic theory, and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime.