Entropy current for non-relativistic fluid

TL;DR

This paper derives the entropy current and constrains transport coefficients for a non-relativistic, parity-odd charged fluid in electromagnetic fields by reducing a relativistic fluid and ensuring thermodynamic consistency.

Contribution

It introduces a canonical form of the entropy current for non-relativistic fluids and determines parity-odd transport coefficients consistent with the second law of thermodynamics.

Findings

Established a canonical entropy current for non-relativistic fluids.

Derived constraints on parity-odd transport coefficients.

Ensured second law compliance for the fluid's transport properties.

Abstract

We study transport properties of a parity-odd, non-relativistic charged fluid in presence of background electric and magnetic fields. To obtain stress tensor and charged current for the non-relativistic system we start with the most generic relativistic fluid, living in one higher dimension and reduce the constituent equations along the light-cone direction. We also reduce the equation satisfied by the entropy current of the relativistic theory and obtain a consistent entropy current for the non-relativistic system (we call it "canonical form" of the entropy current). Demanding that the non-relativistic fluid satisfies the second law of thermodynamics we impose constraints on various first order transport coefficients. For parity even fluid, this is straight forward; it tells us positive definiteness of different transport coefficients like viscosity, thermal conductivity, electric conductivity etc. However for parity-odd fluid, canonical form of the entropy current fails to confirm the second law of thermodynamics. Therefore, we need to add two parity-odd vectors to the entropy current with arbitrary coefficients. Upon demanding the validity of second law, we see that one can fix these two coefficients exactly.