Unlike the lost work formulation, this version of the theorem holds for both the system (the control volume) and for its surroundings (the environment and the thermal reservoirs) separately: ψ ψ ˙ ˙ d , s y s = T 0 S ˙ ˙ g , s y s and ψ ψ ˙ ˙ d , s u r r = T 0 S ˙ ˙ g , s u r r where the index "sys" denotes quantities produced within or by the system itself, and "surr" within or by the surroundings. Therefore, summing these two forms, the theorem also holds for the thermodynamic universe as a whole: ψ ψ ˙ ˙ d , t o t = ψ ψ ˙ ˙ d , s y s + ψ ψ ˙ ˙ d , s u r r = T 0 S ˙ ˙ g , s y s + T 0 S ˙ ˙ g , s u r r = T 0 S ˙ ˙ g , t o t where the index "tot" denotes the total quantities of the entire universe.