Optimal Allocation of Replicas to Processors in Parallel Tempering Simulations

The optimal allocation of replicas to a homogeneous or heterogenous set of processors is derived for parallel tempering simulations on multi-processor machines. In the general case, it is possible without substantially increasing wall clock time to achieve nearly perfect utilization of CPU time. Random fluctuations in the execution times of each of the replicas do not significantly degrade the performance of the scheduler.