Parallel Tempering Simulation on Generalized Canonical Ensemble

Parallel tempering simulation is widely used in enhanced sampling of systems with complex energy surfaces. We hereby introduce generalized canonical ensemble (GCE) instead of the usual canonical ensemble into the parallel tempering to further improve abilities of the simulation technique. GCE utilizes an adapted weight function to obtain a unimodal energy distribution even in phase-coexisting region and then the parallel tempering on GCE yields the steady swap acceptance rates (SARs) instead of the fluctuated SARs in that on canonical ensemble. With the steady SARs, we can facilitate assign the parameters of the parallel tempering simulation to more efficiently reach equilibrium among different phases. We illustrate the parallel tempering simulation on GCE in the phase-coexisting region of 2-dimensional Potts model, a benchmark system for new simulation method developing. The result indicates that the new parallel tempering method is more efficient to estimate statistical quantities (i.e., to sample the conformational space) than the normal parallel tempering, specially in phase-coexisting regions of larger systems.

A Hamiltonian Approach for Tsallis Thermostatistics

Since the pioneering work of Tsallis in 1988 [15] in which a nonextensive generalization of the Boltzmann-Gibbs (BG) formalism for statistical mechanics was proposed, intensive research has been dedicated to the development of the conceptual framework behind this new thermodynamical approach and to its application to realistic physical systems. In order to justify the Tsallis generalization, it has been frequently argued that the BG statistical mechanics has a domain of applicability restricted to systems with short-range interactions and non-(multi)fractal boundary conditions [14]. Moreover, it has been recalled that anomalies displayed by mesoscopic dissipative systems and strongly non- Markovian processes represent clear evidence of the departure from BG thermostatistics. These types of arguments have been duly reinforced by recent convincing examples of physical systems that are far better described in terms of the generalized formalism than in the usual context of the BG thermodynamics (see Tsallis [14] and references therein). It thus became evident that the intrinsic nonlinear features present in the Tsallis formalism that lead naturally to power laws represent powerful ingredients for the description of complex systems. In the majority of studies dealing with the Tsallis thermostatistics, the starting point is the expression for the generalized entropy S<sub>q<sub>, where A; is a positive constant, q a parameter, and / is the probability distribution. Under a different framework, some interesting studies [8] have shown that the parameter q can be somehow linked to the system sensibility on initial conditions. Few works have been committed to substantiate the form of entropy (1) in physical systems based entirely on first principles [1, 13]. For example, it has been demonstrated that it is possible to develop dynamical thermostat schemes that are compatible with the generalized canonical ensemble [12].