Entropy change with elevation

I have seen in a number of thermodynamics lectures that the entropy change of a system as it falls approximately isothermally from some height h to the ground is: ΔS = mgh/T



(The proof basically has you conceive of a reversible process between the same two states where some upwards force acts against the force of gravity in order to maintain quasi-mechanical equilibrium. Once the object hits the ground in this theoretical reversible process, it must be heated by Q=mgh to account for the work done by the object on the additional force. With the heat added, the final state of the system in the reversible process matches that in the actual process. The change in entropy is thus Q_rev/T = mgh/T. I can explain this in more detail if needed.)



My question: how come we don't take change in entropy associated with change in height into account in the open system entropy balance? Every textbook I have seen accounts for only entropy inflow due to mass flowing in, entropy inflow due to heat transfer in, and entropy outflow due to mass flowing out.



But why is there no mgh/T term for change in elevation?



Thanks in advance!