Abstract
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. Finally we extended it to its most general form, consistent with the principle of local entropy production. As a by-product we got the constraints on the second order transport coefficients for a parity even charged fluid, but in some non-standard fluid frame.
Highlights
Fluid dynamics is an effective description for near equilibrium physics
Once we have chosen a form of Sμ, our goal would be to add appropriate terms to the entropy current so that full divergence could be re-expressed as sum of squares upto the required order in derivative expansion
We assumed that the entropy current should be such that its divergence is always positive definite on any solution of fluid equations
Summary
Fluid dynamics is an effective description for near equilibrium physics. In the ‘fluid limit’, it is possible to describe the system only by a few classical functions (much fewer than the number of degrees of freedom, the underlying microscopic theory has). Though the main purpose of this note is just to show how the algorithm described in [11] works out, this analysis will implicitly generate a new set of physical constraints to be imposed on the transport coefficients of charged fluid at second order in derivative expansion. This set of constraints itself could be important in the context of high energy physics. Our analysis will be restricted only to the parity even sector of the charged fluid
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