In the past decades, computer simulations have been firmly established as a powerful research tool in fields ranging from statistical physics to physical chemistry, from polymer to computer science. Many interesting systems, however, exhibit a rugged free energy landscape with a structure of multiple valleys separated by barriers, whose presence entails extremely large relaxation times and thus constitutes the one most severe obstacle for the efficient simulation of complex systems. Here the introduction of generalized ensemble techniques has improved the efficiency of simulation techniques by several orders of magnitude, additionally allowing for a direct estimate of the free energy useful in many contexts.
The Monte Carlo method is one of the central tools of numerical integration, by now employed in a vast number of fields of research. Based on the principle of detailed balance, the Metropolis-Hastings algorithm is the workhorse of the Monte Carlo technique. Under its guidance the system performs a (biased) random walk in configuration space. While this is perfectly acceptable for sampling the localized canonical distribution, in generalized-ensemble simulations one attempts to visit states of all energies, magnetizations, reaction coordinates etc. with equal (or comparable) probability. At this point, the diffusive behavior of the standard Metropolis based approaches regularly turns into the dominant bottleneck of the simulation since equally sampling an extensive phase space volume becomes prohibitively slow.
Detailed balance, however, is not a necessary condition for a Monte Carlo scheme to work. In principle, global balance is sufficient. Relatively little research has been undertaken to date, however, to explore schemes violating detailed while retaining global balance, which might lead to improved convergence properties. In the current project, we study the applicability of non-reversible sampling techniques to improving the diffusive sampling speed in flat-histogram Monte Carlo simulations.