  We present a thermodynamically consistent method by which equations of state
based on nonrelativistic potential models can be modified so that they respect
causality at high densities, both at zero and finite temperature (entropy). We
illustrate the application of the method using the high density phase
parametrization of the well known APR model in its pure neutron matter
configuration as an example. We also show that, for models with only contact
interactions, the adiabatic speed of sound is independent of the temperature in
the limit of very large temperature. This feature is approximately valid for
models with finite-range interactions as well, insofar as the temperature
dependence they introduce to the Landau effective mass is weak. In addition,
our study reveals that in first principle nonrelativistic models of hot and
dense matter, contributions from higher than two-body interactions must be
screened at high density to preserve causality.
