  A key issue in fluid dynamics is the unique definition of the phase-space
Lagrangian dynamics characterizing prescribed ideal fluids (i.e., continua),
which is related to the dynamics of so-called \textit{ideal tracer particles}
(ITP) moving in the same fluids. These are by definition particles of
infinitesimal size which do not produce significant perturbations of the fluid
fields and do not interact among themselves. For Navier-Stokes (NS) fluids, the
discovery by Tessarotto et al. (2005-2009) of the phase-space dynamical system
advancing in time the state of the fluid, has made possible, \textit{in the
case NS fluids}, the actual definition of these trajectories. In this paper we
intend to pose the problem in the case of compressible/incompressible
magnetofluids based on the inverse kinetic theory which can be developed for
their phase-space statistical description (see also accompanying paper) \ We
propose the conjecture of the existence of a subset of ITP's (i.e., particular
solutions of the phase-space dynamical system), denoted as \textit{thermal
ideal tracer particles} (TITP). These particles are characterized by a relative
velocity with respect to the fluid, whose magnitude is determined, by the
kinetic pressure (in turn, related to the fluid pressure).
