  We derive the finite-temperature quantum-tunneling rate from first
principles. The rate depends on both real- and imaginary-time; we demonstrate
that the relevant instantons should therefore be defined on a Schwinger-Keldysh
contour, and how the familiar Euclidean-time result arises from it in the limit
of large physical times. We generalize previous results for general initial
states, and identify distinct behavior in the high- and low-temperature limits,
incorporating effects from background fields. We construct a consistent
perturbative scheme that incorporates large finite-temperature effects.
