  Annealing has proven highly successful in finding minima in a cost landscape.
Yet, depending on the landscape, systems often converge towards local minima
rather than global ones. In this Letter, we analyse the conditions for which
annealing is approximately successful in finite time. We connect annealing to
stochastic thermodynamics to derive a general bound on the distance between the
system state at the end of the annealing and the ground state of the landscape.
This distance depends on the amount of state updates of the system and the
accumulation of non-equilibrium energy, two protocol and energy landscape
dependent quantities which we show are in a trade-off relation. We describe how
to bound the two quantities both analytically and physically. This offers a
general approach to assess the performance of annealing from accessible
parameters, both for simulated and physical implementations.
