An algorithm is presented which enables the direct simulation of isenthalpic pressure changes and isobaric enthalpy changes using molecular dynamics (MD). The pressure and enthalpy can be controlled using either a constraint or extended system formalism. By controlling the rate with which new state points are approached, reversible or irreversible thermodynamic cycles can be simulated directly. The method can be incorporated easily into a standard MD algorithm, and provides a means for rapidly driving a system to a desired thermodynamic statepoint. In a companion paper [1], the method is applied to compute thermodynarnic derivatives, simulate a vapor compression refrigeration cycle, and compute vapor-liquid coexistence curves.