 Entropy generation in finite-temperature heat transfer

When a system at instantaneous temperature $T$ absorbs heat $dQ$ from a reservoir at $T_R$, with no other entropy production in the system, its entropy increases by $dQ/T$ while the reservoir changes by $-dQ/T_R$. The total is positive for spontaneous heat transfer across a finite temperature difference. A quasistatic mechanical path can therefore be thermally irreversible.