The theoretical framework for a new nonheating method of determining absolute ancient magnetic field intensities (paleointensities) is described. The approach is based on a thermally activated Preisach model for interacting, randomly orientated single-domain grains with uniaxial anisotropy. The model includes theoretical features not accommodated by previous nonheating paleointensity methods; for example, it includes magnetostatic interactions, allows for variable cooling rates, and can identify, isolate, and reject unstable remanence carriers, i.e., multidomain and superparamagnetic contributions. The input Preisach distribution from which the acquisition of a thermal remanent magnetization (TRM) of a given rock sample can be simulated is obtained from information contained in the sample's first-order reversal curve distribution. The paleointensity estimate is determined by comparing the alternating field demagnetization spectrum of the sample's natural remanent magnetization and its simulated TRM. In the companion paper, the protocol is rigorously tested using a suite of historical samples.