Transitions and transport for a spatially periodic stochastic system with locally coupled oscillators

Abstract

In this paper, with a special model, we investigate the spatially periodic stochastic system with locally coupled oscillators subject to a constant force F. A nonequilibrium second-order phase transition is found when F=0. This phase transition is reentrant when the additive noise is weak. With varying the constant force F, a continuous or discontinuous transition between the states with positive and negative mean fields (mu>0 and mu<0) is observed, which is not a phase transition. The mean field or current sometimes exhibits hysteresis as a function of F. With the variation of the force F, when hysteresis of the mean field or current versus F appears, a nonzero probability current with definite direction will occur at the point F=0. The correlation between the additive and multiplicative noises has an effect on the transitions and the transport.

Nonequilibrium Energy Transduction in Stochastic Strongly Coupled Rotary Motors

“…While Suñé and Imparato studied the efficiency of a similar machine with no energy barriers, finding that tight coupling is necessary to approach reversible efficiency, our results imply that there is more to the story when energy barriers are present, which is in line with a number of stochastic machine models that consider strong coupling: A maximum in probability current at strong coupling has been observed in a ratchet model for the mechanochemical coupling between molecular motors and ATP hydrolysis, in a Brownian heat engine composed of two coupled particles, and in coupled stochastic oscillators . These findings suggest that intermediate-strength coupling can be valuable in a wide range of systems.…”

“…20 These are 4−12× larger and hence consistent as upper bounds with our simple theoretical prediction (eq 6) that at physiological conditions (μ H + = 10 k B T/rad, −μ H + /μ ATP = 1.1) the power-maximizing While Sunẽ́and Imparato 34 studied the efficiency of a similar machine with no energy barriers, finding that tight coupling is necessary to approach reversible efficiency, our results imply that there is more to the story when energy barriers are present, which is in line with a number of stochastic machine models that consider strong coupling: A maximum in probability current at strong coupling has been observed in a ratchet model for the mechanochemical coupling between molecular motors and ATP hydrolysis, 35 in a Brownian heat engine composed of two coupled particles, 36 and in coupled stochastic oscillators. 37 These findings suggest that intermediate-strength coupling can be valuable in a wide range of systems. Here, we systematically study a range of coupling strengths between subsystems and explicitly consider the consequences for the design principles of molecular machines.…”

Nonequilibrium Energy Transduction in Stochastic Strongly Coupled Rotary Motors

“…While Suñe and Imparato 32 studied the efficiency of a similar machine with no energy barriers, finding that tight coupling is necessary to approach reversible efficiency, our results imply that there is more to the story when energy barriers are present, which is in line with a number of stochastic machine models that consider strong coupling: A maximum in probability current at strong coupling has been observed in a ratchet model for the mechanochemical coupling between molecular motors and ATP hydrolysis, 33 in a Brownian heat engine composed of two coupled particles, 34 and in coupled stochastic oscillators. 35 These findings suggest that intermediate-strength coupling can be valuable in a wide range of systems. Here, we systematically study a range of coupling strengths between subsystems, and explicitly consider the consequences for the design principles of molecular machines.…”