Brownian ratchets and pumps can universally approximate any local active dynamics in spin systems by harnessing heat currents or periodic driving.
Zwanzig,Nonequilibrium Statistical Mechanics(Ox- ford University Press, Oxford, 2001)
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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.
A topological argument shows the fluctuation-dissipation relation holds exactly for nonlinear Navier-Stokes, proving the GENERIC decomposition and producing a well-posed stochastic completion with physical cutoff.
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Brownian ratchets and pumps universally simulate many-body active dynamics
Brownian ratchets and pumps can universally approximate any local active dynamics in spin systems by harnessing heat currents or periodic driving.
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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.
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Physical completion of the Navier-Stokes equations
A topological argument shows the fluctuation-dissipation relation holds exactly for nonlinear Navier-Stokes, proving the GENERIC decomposition and producing a well-posed stochastic completion with physical cutoff.
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