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Register a new userGeneralized-Ensemble Algorithms for the Isobaric-Isothermal Ensemble
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We present generalized-ensemble algorithms for isobaric-isothermal molecular simulations. In addition to the multibaric-multithermal algorithm and replica-exchange method for the isobaric-isothermal ensemble, which have already been proposed, we propose a simulated tempering method for this ensemble. We performed molecular dynamics simulations with these algorithms for an alanine dipeptide system in explicit water molecules to test the effectiveness of the algorithms. We found that these generalized-ensemble algorithms are all useful for conformational sampling of biomolecular systems in the isobaric-isothermal ensemble.
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We review uses of the generalized-ensemble algorithms for free-energy calculations in protein folding. Two of the well-known methods are multicanonical algorithm and replica-exchange method; the latter is also referred to as parallel tempering. We present a new generalized-ensemble algorithm that combines the merits of the two methods; it is referred to as the replica-exchange multicanonical algorithm. We also give a multidimensional extension of the replica-exchange method. Its realization as an umbrella sampling method, which we refer to as the replica-exchange umbrella sampling, is a powerful algorithm that can give free energy in wide reaction coordinate space.
In this work, we show that the dissipation in a many-body system under an arbitrary non-equilibrium process is related to the R{e}nyi divergences between two states along the forward and reversed dynamics under very general family of initial conditions. This relation generalizes the links between dissipated work and Renyi divergences to quantum systems with conserved quantities whose equilibrium state is described by the generalized Gibbs ensemble. The relation is applicable for quantum systems with conserved quantities and can be applied to protocols driving the system between integrable and chaotic regimes. We demonstrate our ideas by considering the one-dimensional transverse quantum Ising model which is driven out of equilibrium by the instantaneous switching of the transverse magnetic field.
The local physical properties of an isolated quantum statistical system in the stationary state reached long after a quench are generically described by the Gibbs ensemble, which involves only its Hamiltonian and the temperature as a parameter. If the system is instead integrable, additional quantities conserved by the dynamics intervene in the description of the stationary state. The resulting generalized Gibbs ensemble involves a number of temperature-like parameters, the determination of which is practically difficult. Here we argue that in a number of simple models these parameters can be effectively determined by using fluctuation-dissipation relationships between response and correlation functions of natural observables, quantities which are accessible in experiments.
We propose a method to extend the fast on-the-fly weight determination scheme for simulated tempering to two-dimensional space including not only temperature but also pressure. During the simulated tempering simulation, weight parameters for temperature-update and pressure-update are self-updated independently according to the trapezoidal rule. In order to test the effectiveness of the algorithm, we applied our proposed method to a peptide, chignolin, in explicit water. After setting all weight parameters to zero, the weight parameters were quickly determined during the simulation. The simulation realised a uniform random walk in the entire temperature-pressure space.
We propose explicit symplectic integrators of molecular dynamics (MD) algorithms for rigid-body molecules in the canonical and isothermal-isobaric ensembles. We also present a symplectic algorithm in the constant normal pressure and lateral surface area ensemble and that combined with the Parrinello-Rahman algorithm. Employing the symplectic integrators for MD algorithms, there is a conserved quantity which is close to Hamiltonian. Therefore, we can perform a MD simulation more stably than by conventional nonsymplectic algorithms. We applied this algorithm to a TIP3P pure water system at 300 K and compared the time evolution of the Hamiltonian with those by the nonsymplectic algorithms. We found that the Hamiltonian was conserved well by the symplectic algorithm even for a time step of 4 fs. This time step is longer than typical values of 0.5-2 fs which are used by the conventional nonsymplectic algorithms.
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