We review the key steps of relativistic fluid dynamics formalism with spin degrees freedom initiated recently. obtain equations motion expansion system from underlying definitions quantum kinetic theory for equilibrium phase space distribution functions. investigate polarization in Bjorken hydrodynamical background.

We introduce a higher-dimensional version of the nonlinear thermodynamic formalism introduced by Buzzi and Leplaideur, in which potential is replaced family potentials. In particular, we establish corresponding variational principle discuss existence, characterization, number equilibrium measures for this version.