The possibly very long but nevertheless finite time it takes for an isolated dynamical system of finite volume described by Newtonian mechanics and subject to conservative forces (see conservative field) to return to a state arbitrarily close to the initial state. This time tends to infinity as the volume tends to infinity. The existence of the Poincaré recurrence time was proved by Henri Poincaré in 1890. There is an analogue of this result in quantum mechanics. The concept of the Poincaré recurrence time has been discussed extensively in the contexts of the foundations of dynamical systems and statistical mechanics.