We present a new context independent complexity measure, the information capacitance, for discrete probability distributions, which is based on entropy- and energy measures and describes the ability of a system to absorb or emit information. We compare the new complexity measure with the statistical definition of complexity given by Lopez-Ruiz, Mancini and Calbet. We apply both definitions in several systems which are described by discrete probability distributions. Namely, two systems beyond the thermodynamic equilibrium, i.e. a DNA-two state system and the logistic map, and also for magnetic systems in thermodynamic equilibrium. It is shown that the information capacitance takes into account spin fluctuations near phase transitions in magnetic systems.