Derives exact thermal noise for nonlinear Navier-Stokes via Poincaré's lemma, proving GENERIC reversible/irreversible split and global well-posedness of the stochastic system with physical cutoff.
Zwanzig,Nonequilibrium Statistical Mechanics(Ox- ford University Press, Oxford, 2001)
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cond-mat.stat-mech 2years
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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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Physical completion of the Navier-Stokes equations
Derives exact thermal noise for nonlinear Navier-Stokes via Poincaré's lemma, proving GENERIC reversible/irreversible split and global well-posedness of the stochastic system with physical cutoff.
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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.