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We present a novel method for the calculation of the energy density of states D(E) for systems described by classical statistical mechanics. The method builds on an extension of a recently proposed strategy that allows the free energy profile of a canonical system to be recovered within a pre-assigned accuracy,[A. Laio and M. Parrinello, PNAS 2002]. The method allows a good control over the error on the recovered system entropy. This fact is exploited to obtain D(E) more efficiently by combining measurements at different temperatures. The accuracy and efficiency of the method are tested for the two-dimensional Ising model (up to size 50x50) by comparison with both exact results and previous studies. This method is a general one and should be applicable to more realistic model systems.
Sampling complex potential energies is one of the most pressing challenges of contemporary computational science. Inspired by recent efforts that use quantum effects and discretized Feynmans path integrals to overcome large barriers we propose a repl
It is shown that the algorithm introduced in [1] and conceived to deal with continuous degrees of freedom models is well suited to compute the density of states in models with a discrete energy spectrum too. The q=10 D=2 Potts model is considered as
For a classical system of noninteracting particles we establish recursive integral equations for the density of states on the microcanonical ensemble. The recursion can be either on the number of particles or on the dimension of the system. The solut
In this paper we propose a new formalism to map history-dependent metadynamics in a Markovian process. We apply this formalism to a model Langevin dynamics and determine the equilibrium distribution of a collection of simulations. We demonstrate that
Since the Time-Dependent Density Functional Theory is mathematically formulated through non-linear coupled time-dependent 3-dimensional partial differential equations it is natural to expect a strong sensitivity of its solutions to variations of the