Entropy Current from Partition Function: One Example

Understand

In hydrodynamics the existence of an entropy current with non-negative divergence is related to the existence of a time-independent solution in a static background.

• Recently there has been a proposal for how to construct an entropy current from the equilibrium partition function of the fluid system.
• In this note, we have applied this algorithm for the charged fluid at second order in derivative expansion.
• From the partition function we first constructed one example of entropy current with non-negative divergence upto the required order.