  Various forms of exact laws governing magnetohydrodynamic (MHD) turbulence
have been derived either in the incompressibility limit, or for isothermal
compressible flows. Here we propose a more general method that allows us to
obtain such laws for any turbulent isentropic flow (i.e., constant entropy). We
demonstrate that the known MHD exact laws (incompressible and isothermal) and
the new (polytropic) one can be obtained as specific cases of the general law
when the corresponding closure equation is stated. We also recover all known
exact laws of hydrodynamic (HD) turbulence (incompressible, isothermal and
polytropic) from this law in the limit ${\bf B}=0$. We furthermore show that
the difference between the two forms (isothermal and polytropic) of the MHD
exact laws of interest in this work resides in some of the source terms and in
the explicit form of the flux term that depends on internal energy. Finally, we
apply these two forms to Parker Solar Probe (PSP) data taken in the inner
heliosphere to highlight how the different closure equations affect the energy
cascade rate estimates.
