Transpulmonary pressure is the difference in pressure the inside of the lungs (alveolar pressure) and outside of the lung (intrapleural pressure). When it says outside the lung it means the area/fluid between the lung and the thoracic wall.
The pressure of the intrapleural fluid affects pressure in the alveoli. The difference between pressure in the alveoli and and atmospheric pressure is what causes ventilation of the lungs. So this means at the end of expiration the atmospheric pressure will equal the alveolar pressure. So if the alveolar pressure is 0 (the same as atmospheric) then would it not collapse? Nope as the collapsing is prevented by the negative pressure of the intrapleural fluid/cavity.
Inspiration = Thorax expands - Intrapleural pressure gets more negative - this causes transpulmonary pressure to increase - so the lungs expand and alveolar pressure becomes lower than that of the atmosphere - so air flows in.
In pneumothorax the thorax is penetrated so air enters this intrapleural cavity. The pressure of the intrapleural cavity will no longer be negative, causing the thorax to widen and the lung to collapse. I think its common in horses, treated by removing the air from the interpleural space, well as much as possible. This makes the intrapleural space negative again. Whatever small amount of air that is left will be absorbed by the tissues.
Never heard of that equaling the elastic recoil of the lung. Unless you mean complaince of the lung (stretchability) and that equals the change in volume over transpulmonary pressure.
Hope I helped and wasn't too confusing
