Non-Isolated System

System at $T_{H} > T_{L}$
$\Rightarrow δ Q < 0$ (heat loss)
$d S_{s y s} \geq \frac{δ Q}{T_{H}}$
$d S_{o u t} \geq \frac{- δ Q}{T_{L}}$
$d S_{o u t} + d S_{s y s} \geq 0 \geq δ Q (\frac{1}{T_{H}} - \frac{1}{T_{L}})$