Apatite fission track length distributions and ages provide an integrated record of the low-temperature (~20¿--150 ¿C) thermal history of the host rock over geologic time scales. The information content of these data is quantified by applying a stochastic optimization technique (simulated annealing) to determine the range of thermal histories compatible with synthetic apatite fission track data given a mathematical description of fission track annealing. The goodness of fit between the observed and predicted data parameters and a slowly decreasing control parameter are treated as analogous to the free energy and temperature, respectively, of a thermodynamic system. On this basis a Boltzmann-type probability distribution is defined and used to accept or reject random thermal history perturbations. A priori information used to constrain the model space may include the temperature range in which the solutions are sought, present-day temperature, the complexity of the thermal history, and the maximum duration of the data-sensitive thermal history. This approach allows determination of the range of thermal histories compatible with an observed confined track length distribution and associated fission track age, and it provides an estimate of the probability distribution of temperatures at a specific time. Results for synthetic data sets for diverse model thermal histories suggest that the resolution of thermal history is generally poor; parts of the thermal history to which the data are most sensitive can be resolved to no better than about ¿10 ¿C for ideal data. Bounds on acceptable time-temperature space are sensitive to the assumed complexity of the thermal history but are relatively insensitive to typical uncertainties associated with the data. Application of this approach to real data is fundamentally limited by the uncertainty associated with extrapolating annealing models to geologic conditions. ¿1991 American Geophysical Union