  We consider one-loop quantum corrections to the thermodynamics of a black
hole in generic 2-dimensional dilaton gravity. The classical action is the most
general diffeomorphism invariant action in 1+1 space-time dimensions that
contains a metric, dilaton, and Abelian gauge field, and having at most second
derivatives of the fields. Quantum corrections are introduced by considering
the effect of matter fields conformally coupled to the metric and non-minimally
coupled to the dilaton. Back reaction of the matter fields (via non-vanishing
trace conformal anomaly) leads to quantum corrections to the black hole
geometry. Quantum corrections also lead to modifications in the gravitational
action and hence in expressions for thermodynamic quantities. One-loop
corrections to both geometry and thermodynamics (energy, entropy) are
calculated for the generic dilaton theory. This formalism is applied to a
charged black hole in spherically symmetric gravity and to a rotating BTZ black
hole.
