Entropy current for non-relativistic fluid

Understand

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.