Extending Hamilton's principle with the second law axiom produces thermodynamically consistent stochastic field theories featuring natural fluctuation-dissipation relations and standard entropy production in extended phase space.
Risken,The Fokker-Planck Equation: Methods of Solution and Applications(Springer Berlin Heidelberg, 1996)
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Derives duality between dissipation-coherence trade-off and thermodynamic speed limit for general stochastic limit cycles via dual observables substituted into the thermodynamic uncertainty relation in the weak-noise limit.
A unified geometric variational formulation based on nonlinear nonholonomic constraints derives a thermodynamically consistent stochastic thermodynamics with entropy as a dynamical variable and naturally emerging fluctuation theorems.
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A variational formulation of stochastic thermodynamics: Spatially extended systems
Extending Hamilton's principle with the second law axiom produces thermodynamically consistent stochastic field theories featuring natural fluctuation-dissipation relations and standard entropy production in extended phase space.
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Duality between dissipation-coherence trade-off and thermodynamic speed limit based on thermodynamic uncertainty relation for stochastic limit cycles
Derives duality between dissipation-coherence trade-off and thermodynamic speed limit for general stochastic limit cycles via dual observables substituted into the thermodynamic uncertainty relation in the weak-noise limit.
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Variational formulation of stochastic thermodynamics: Finite-dimensional systems
A unified geometric variational formulation based on nonlinear nonholonomic constraints derives a thermodynamically consistent stochastic thermodynamics with entropy as a dynamical variable and naturally emerging fluctuation theorems.