Connecting fluctuation-dissipation ideas to synchronization in equilibrium and nonequilibrium systems

Nonequilibrium systems have both fundamental and technological interest for their unusual behavior, but surprisingly little research effort has been put into diagnosing how far a system is from equilibrium. Here, we show a connection between Langevin synchronization ideas and the position auto-correlation function. We present results for the thermalization timescale of a particle in equilibrium or out-of-equilibrium while coupled to heat a reservoir. In the out-of-equilibrium system the particle is driven away from equilibrium by a time-dependent potential.