*6.1. Relation to DynMaxEnt*

Consider state variables **x** = (**r**, **p**) as in the Section 3.3 on the damped particle (disregarding entropy for simplicity). The Poisson bivector is then canonical, **L** = \$ 0 1 −1 0% , and the dissipation potential is quadratic in conjugate momentum, Ξ = <sup>1</sup> <sup>2</sup>*<sup>τ</sup>* (**p**∗)2. This conjugate momentum, according to Equation (89b), approaches the value where GENERIC evolution equations hold, Equation (11), and eventually reaches the value given by the derivative of thermodynamic potential.

Now, assume that state variable **p** evolves faster to the corresponding equilibrium (zero) than both **r** and conjugate variables. The GENERIC evolution equations then become Equations (11a) and (15). The conjugate variable **p**∗ approaches the value where the GENERIC equations are valid, which means that it approaches solutions to Equation (15) as in the DynMaxEnt procedure. Conjugate variables approach the Gibbs–Legendre manifold (80). Contact geometry provides motivation and geometric meaning to the Dynamic MaxEnt reduction.
