Statistical mechanics of a coupled oscillator system with a coupling function containing higher harmonic components

摘要

We analyzed associative memory models consisting of coupled oscillators with coupling functions containing higher harmonic components. It used to be believed that two types of XY-spin systems, one governed by continuous dynamics. i.e., coupled oscillators and one done by sequential dynamics, have identical macroscopic properties in equilibrium states, since they have the same free energy. Therefore, everybody has believed that statistical mechanical methods for analyzing sequential XY-spin systems can be directly applyed to coupled oscillators. We found that, by deriving macroscopic dynamical theories from the system with higher harmonic components. coupled oscillator systems do not obey the Maxwell rule, which holds in sequential XY-spin systems. This is because, in microscopic level, each oscillator's configuration can hot jump over microscopic energy barriers, hampered by the microscopic memory effect. According to this result, we can conclude that there are mistakes in almost theories based on the Maxwell rule that are used to treat coupled oscillator systems.