Random number generation with the recursion Xt=Xt-3p⊕Xt-3q
Journal of Computational and Applied Mathematics - Random numbers and simulation
Quantum chaos: a decoherent definition
Papers from the 14th annual international conference of the Center for Nonlinear Studies on Quantum complexity in mesoscopic systems
Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems
Journal of Computational Physics
Temporal acceleration of spatially distributed kinetic Monte Carlo simulations
Journal of Computational Physics
Time Reversibility, Computer Simulation, and Chaos
Time Reversibility, Computer Simulation, and Chaos
Hi-index | 31.45 |
This study addresses the initial-boundary value problem of coarse-grained probability measure on the state space in which a differentiable vector field v is given and, as a consequence, the differenced continuity equation using the first-order upwind difference scheme (UDS) based on the finite volume method appears as the physical substance on the coarse-grained dynamics. At first, the UDS is theoretically shown to be equivalent to a class of coarse-grained master equations (CGME), brought by a principle that we cannot distinguish state points in the same partition with each other. The principle is based on the formulation of non-equilibrium statistical mechanics to resolve the macroscopic irreversibility. Moreover the entropy production evaluated by the UDS is also shown to be in accord with the average volume contraction rate in the steady state. This is essential for the non-equilibrium statistical dynamics and was numerically confirmed. Under the principle of coarse graining the UDS is very superior to the conventional Monte-Carlo method in computer time and storage and is very useful to solve the CGME.