Serial tempering without exchange

Serial tempering is a computational method that turns the temperature T (or more generally any independent λ parameter) into a dynamical variable. It is shown that, under conditions for which this variable is fast, serial tempering is equivalent to the umbrella sampling method with a single effective potential. This equivalence is demonstrated using both a small one-dimensional system and a small solvated peptide. The suggestion is then made to replace the serial tempering protocol with the equivalent umbrella sampling calculation. This approach, serial tempering without exchange (STeWiE), has the same performance as serial tempering in the limit that exchanges are frequent, is simpler to implement, and has fewer adjustable parameters than conventional serial tempering. The equivalence of serial tempering and STeWiE also provides a convenient route for estimating and optimizing the performance of serial tempering simulations and other generalized-ensemble methods.