  It is shown that adding hair like electric charge or angular momentum to the
black hole decreases the amount of entropy emission. This motivates us to study
the emission rate of entropy from black holes and conjecture a maximum limit
(upper bound) on the rate of local entropy emission ($\dot{S}$) for thermal
systems in four dimensional space time and argue that this upper bound is
$\dot{S}\simeq k_{B} \sqrt{\frac{c^5}{\hbar G}}$. Also by considering R\`{e}nyi
entropy, it is shown that Bekenstein-Hawking entropy leads to a maximum limit
for the rate of entropy emission. We also suggest an upper bound on the surface
gravity of the black holes which is called Planck surface gravity. Finally we
obtain a relation between maximum rate of entropy emission, Planck surface
gravity and Planck temperature of black holes.
