In a reversible or quasi-static, idealized process of transfer of energy as heat to a closed thermodynamic system of interest, (which allows the entry or exit of energy – but not transfer of matter), from an auxiliary thermodynamic system, an infinitesimal increment ( d S ) in the entropy of the system of interest is defined to result from an infinitesimal transfer of heat ( δ δ Q ) to the system of interest, divided by the common thermodynamic temperature ( T ) of the system of interest and the auxiliary thermodynamic system: