HEP Theory Journal Club

The principle of stationary nonconservative action: basic formalism and the Navier-Stokes action

Dave Tsang

Hamilton's principle of stationary action is a cornerstone of mathematical physics, however it is generally inapplicable to nonconservative systems. I will present a new formalism that addresses this longstanding issue, allowing generic nonconservative systems to be represented in an action formulation. A generalized Noether's theorem can be derived for describing Noether current evolution in general nonconservative systems. Examples of both nonconservative discrete mechanics and nonconservative classical field theories will be discussed, including the development of an action for a Navier-Stokes fluid including heat diffusion. Remarkably, this approach naturally allows for non-equilibrium thermodynamic processes to be described by an unconstrained action. Numerical applications of this formalism, i.e. nonconservative variational integrators, will also be discussed if time permits.