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Entropy and Heat Conduction

  Differences in the bulk velocities of the photons and baryons $\Theta_1^{(m)} - v_B^{(m)}$ also represent imperfections in the fluid that lead to entropy generation and heat conduction. The baryon Euler equations (67) and (71) give 
{rcl}\displaystyle{}\Theta_1^{(0)}- v_B^{(0)}&...
 ...ot V + {\dot a \over a} (v_B^{(1)}- V)
 \right] \, ,\end{array}\end{displaymath}   
which may be iterated to the desired order in $1/\dot\tau$.For scalar fluctuations, this slippage leads to the generation of non-adiabatic pressure or entropy fluctuations
{rcl}\displaystyle{}\Gamma_{\gamma B} &\equiv ...
 ...R} \int (\Theta_1^{(0)}- v_B^{(0)}) 
 k\, d\eta \, ,\end{array}\end{displaymath}   
as the local number density of baryons to photons changes. Equivalently, this can be viewed as heat conduction in the fluid. For vorticity fluctuations, these processes do not occur since there are no density, pressure, or temperature differentials in the fluid.

Wayne Hu