Symmetry Relations for Trajectories of a Brownian Motor

Abstract

A Brownian Motor is a nanoscale or molecular device that combines the effects of thermal noise, spatial or temporal asymmetry, and directionless input energy to drive directed motion. Because of the input energy, Brownian motors function away from thermodynamic equilibrium and concepts such as linear response theory, fluctuation dissipation relations, and detailed balance do not apply. The {\em generalized} fluctuation-dissipation relation, however, states that even under strongly thermodynamically non-equilibrium conditions the ratio of the probability of a transition to the probability of the time-reverse of that transition is the exponent of the change in the internal energy of the system due to the transition. Here, we derive an extension of the generalized fluctuation dissipation theorem for a Brownian motor for the ratio between the probability for the motor to take a forward step and the probability to take a backward step.

References in corpus (2)

• Brownian motors: noisy transport far from equilibrium
• The unreasonable effectiveness of equilibrium-like theory for interpreting non-equilibrium experiments

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• Fine-structured large deviations and the fluctuation theorem: Molecular motors and beyond
• Interacting molecular motors: Efficiency and work fluctuations
• Entropy and efficiency of a molecular motor model