Uncertainty principle for generalized diffusions
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It is shown that with any generalized diffusion a complementary variable, theprobabilistic group velocity (PGV), can be associated, such that the uncertainties in the position (diffusion) and its complementary PGV (like momentum) satisfy a Heisenberg-type uncertainty relation. It is shown that the bound is achieved in the linear Gaussian case. In the statistical steady state, the PGV vanishes identically. The uncertainty in the PGV is an achievable upper bound to the rate of the RMS value of the diffusion. The PGV is further related to the entropy rate of the diffusion process.
KeywordsEntropy Steady State Field Theory Elementary Particle Quantum Field Theory
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