Fluctuating boundary data in Hamilton's principle propagate via Hamilton-Jacobi to produce state-dependent multiplicative Langevin forces, with additive noise recovered only after Markovian coarse-graining.
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Decoherence leaves complementary quantum (cat-like state with Wigner negativity) and classical (Darwinian which-path) records in the bath, demonstrated via tensor-network simulations of a spin-boson model.
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Variational Boundary Fluctuations as a First-Principles Origin of Langevin Noise
Fluctuating boundary data in Hamilton's principle propagate via Hamilton-Jacobi to produce state-dependent multiplicative Langevin forces, with additive noise recovered only after Markovian coarse-graining.