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arXiv · 1405.5687

Entropy current for non-relativistic fluid

Nabamita Banerjee·Suvankar Dutta·Akash Jain·Dibakar Roychowdhury
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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.

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Nabamita Banerjee, Suvankar Dutta, Akash Jain, Dibakar Roychowdhury. 2014-05-22. Entropy current for non-relativistic fluid. https://doi.org/10.1007/jhep08(2014)037

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