A timepiece mechanism for a secondary display of a first physical quantity, wherein a push-button activates first mechanism for the coupling/uncoupling of the secondary display to or from a movement including a first display, and a pivoting first physical quantity cannon-pinion heart, wherein the first mechanism controls the coupling/uncoupling to or from the movement. A second push-button controls the zero reset of the secondary display, by uncoupling the first coupling/uncoupling mechanism, and returning the heart-piece to the original position thereof. A second coupling/uncoupling control mechanism includes either a pivoting time zone wheel set including a friction wheel, meshing with the movement, and a time zone wheel which, when the wheel set is in the coupling position, drives a second physical quantity cannon-pinion heart and/or a third physical quantity cannon-pinion heart, the friction wheel and time zone wheel being coaxial and cooperating via friction; or an inter-time zone mechanism.