turnpike

1. (Scotland) A winding stairway.Examples: "Ramsay stabbed Ruthven accordingly and James lending his assistance they thrust the wounded man down the turnpike by which Ramsay had ascended Voices and steps were now heard advancing upwards and Ramsay knowing the accents called out to sir Thomas Erskine to come up the turnpike stair even to the head Sir Thomas Erskine was accompanied by sir Hugh Harris the king's physician a lame man and unfit for fighting Near the bottom of the turnpike sir Thomas Erskine in his ascent met Ruthven bleeding in the face and neck and called out Fie strike I this is the traitor l on which Alexander Ruthven was run through the body having only breath remaining to say Alas I had no blame of it"Scotland

2. (military) A beam filled with spikes to obstruct passage; a cheval de frise.

3. (chiefly US) A toll road, especially a toll expressway.Examples: "Eleven Pair of Mills ſtand within Four Miles of the Place, which bring a great Trade to it: But the Road is by this means ſo continually torn, that it is one of the worſt Turnpikes about London."; "[T]here is a bundle of pawnbrokers' duplicates, those turnpike tickets on the road of poverty ..."Synonyms: pikeUS

4. (mathematical economics) A trajectory on a finite time interval that satisfies an optimality criterion which is associated with a cost function.Examples: "In the monograph we discuss a number of results concerning turnpike properties in the calculus of variations and optimal control which were obtained by the author in the last ten years."