The molecular description of friction at a single, ideal microscopic contact of the sort realizable in scanning surface probe devices is greatly complicated by wide variations in the temporal regime t(*)equivalent tot(expt)/t(r) of the measurement, where t(expt) is the time taken to measure the frictional force F-s and t(r) is the time required for the system to attain a state of thermodynamic equilibrium. At one extreme (t(*)>>1) the system remains in equilibrium for the duration of the measurement and one can employ statistical thermodynamics (in practice, Monte Carlo simulation) to compute F-s, which depends only on the thermodynamic state. At the other extreme (t(*)<<1) the system remains out of equilibrium. One must then account for the dynamic history of the system, typically by means of nonequilibrium molecular dynamics. The range of t(*) between these extremes can be handled within a single theoretical framework based on the concept of "equivalent equilibrated states." Through addition of auxiliary potential fields to the Hamiltonian specific degrees of freedom of the system can be constrained. The properties of the constrained system are computed from the free energy of the system trapped in the equivalent equilibrated state by the constraints. The constraints are chosen to correspond to t(*). The results of the theory applied to a one-dimensional model demonstrate dramatically the impact of history on F-s.