# Enforcing causality in nonrelativistic equations of state at finite temperature

## TL;DR

This paper introduces a thermodynamically consistent method to modify nonrelativistic equations of state, ensuring causality at high densities and finite temperatures, with implications for modeling hot, dense matter.

## Contribution

A novel method to enforce causality in nonrelativistic equations of state at finite temperature, demonstrated on the APR model and analyzing effects of interactions and temperature dependence.

## Key findings

- The method ensures causality at high densities for nonrelativistic models.
- In contact interaction models, the speed of sound is temperature-independent at high temperatures.
- Higher than two-body interactions need screening at high densities to maintain causality.

## Abstract

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.