Conciliating synchronicity with spatial discretization, exclusion, interactions, and detailed balance

Area of Science:

• Statistical Mechanics
• Computational Physics
• Complex Systems

Background:

• Simulating discrete stochastic systems with synchronous evolution rules while maintaining detailed balance is challenging.
• Nontrivial interactions often create a conflict between synchronicity and thermodynamic equilibrium.

Purpose of the Study:

• To present a fully synchronous algorithm for simulating particle migration on a lattice.
• To demonstrate that synchronicity and detailed balance can be achieved simultaneously in such systems.

Main Methods:

• Developed parallel Kawasaki dynamics (PKD), a novel synchronous algorithm.
• Incorporated site exclusion, local interactions, and detailed balance without system partitioning.
• Derived a temperature-dependent pseudo-Hamiltonian from the PKD dynamics.

Main Results:

• PKD successfully simulates particle migration with full synchronicity and detailed balance.
• The derived pseudo-Hamiltonian is temperature-dependent.
• Equilibrium properties differ significantly from conventional models near critical conditions.

Conclusions:

• Parallel Kawasaki dynamics offers a viable approach for simulating complex interacting particle systems.
• The temperature-dependent nature of the derived Hamiltonian highlights unique equilibrium properties.
• This method advances the simulation of systems requiring both synchronicity and thermodynamic equilibrium.