where ∮ ∮ d S Res is the total entropy change in the external thermal reservoirs (surroundings), δ δ Q is an infinitesimal amount of heat that is taken from the reservoirs and absorbed by the system ( δ δ Q > 0 if heat from the reservoirs is absorbed by the system, and δ δ Q < 0 if heat is leaving from the system to the reservoirs) and T surr is the common temperature of the reservoirs at a particular instant in time. The closed integral is carried out along a thermodynamic process path from the initial/final state to the same initial/final state (thermodynamic cycle). In principle, the closed integral can start and end at an arbitrary point along the path.