**3. Dynamic MaxEnt**

A form of the Dynamic MaxEnt reduction first appeared in [15] in the context of contact geometry. Here, we further develop DynMaxEnt using the energetic representation, which simplifies the procedure so that reductions, for example, from complex fluid dynamics to Navier–Stokes equation and from hyperbolic heat conduction to the Fourier law are carried out easily. Moreover, we generalize the method to an infinite chain of consecutive approximations.

The key idea behind dynamic MaxEnt is to treat conjugate variables **x**† as independent quantities ensuring invariance of the quasi-equilibrium manifold. This step is motivated by contact geometry, where conjugate variables are indeed granted independence and evolve towards the corresponding Gibbs–Legendre manifold, see Section 6.1.
