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.
Bloch,Nonholonomic Mechanics and Control (Springer New York, 2015)
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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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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.