2007/05/15 by R. Dean Astumian · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Asymmetry #Brownian motion #Brownian motor #Classical mechanics #Detailed balance #Dissipation #Exponential function #Fluctuation theorem #Fluctuation-dissipation theorem #Fractional Brownian motion #Materials science #Mathematical analysis #Mathematics #Molecular motor #Non-equilibrium thermodynamics #Physics #Quantum Information and Cryptography #Quantum mechanics #Statistical physics #Symmetry (geometry) #cond-mat.soft #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.76.020102
arxiv created 2007/05/15 · openalex publication_date 2007/08/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 generalized fluctuation-dissipation relation, however, states that even under strongly thermodynamically nonequilibrium conditions the ratio of the probability of a transition to the probability of the time reverse of that transition is the exponential 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.