Anomalous dynamics triggered by a non-convex equation of state in relativistic flows

TL;DR

This paper investigates how non-convex thermodynamics in dense relativistic matter can lead to complex, anomalous flow dynamics, using a phenomenological equation of state as a simplified model to explore these effects.

Contribution

It introduces a toy-model equation of state with non-convex regions to study relativistic flow dynamics influenced by non-monotonic sound speeds.

Findings

Non-convex EoS can induce anomalous flow behaviors in relativistic hydrodynamics.

A phenomenological EoS constrained by causality and stability can mimic realistic dense matter.

Complex dynamics arise solely from relativistic effects without classical analogs.

Abstract

The non-monotonicity of the local speed of sound in dense matter at baryon number densities much higher than the nuclear saturation density ($n_0 \approx 0.16\,$fm$^{-3}$) suggests the possible existence of a non-convex thermodynamics which will lead to a non-convex dynamics. Here, we explore the rich and complex dynamics that an equation of state (EoS) with non-convex regions in the pressure-density plane may develop as a result of genuinely relativistic effects, without a classical counterpart. To this end, we have introduced a phenomenological EoS, whose parameters can be restricted heeding to causality and thermodynamic stability constraints. This EoS shall be regarded as a toy-model with which we may mimic realistic (and far more complex) EoS of practical use in the realm of Relativistic Hydrodynamics.