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We point out a formal analogy between the Dirac equation in Majorana form andthe discrete-velocity version of the Boltzmann kinetic equation. By asystematic analysis based on the theory of operator splitting, this analogy isshown to turn into a concrete and efficient computational method, providing aunified treatment of relativistic and non-relativistic quantum mechanics. Thismight have potentially far-reaching implications for both classical and quantumcomputing, because it shows that, by splitting time along the three spatialdirections, quantum information (Dirac-Majorana wavefunction) propagates inspace-time as a classical statistical process (Boltzmann distribution).

Formal analogy between the Dirac equation in its Majorana form and the discrete-velocity version of the Boltzmann kinetic equation