TY - JOUR
T1 - Fluctuations of time averages for Langevin dynamics in a binding force field
AU - Dechant, A.
AU - Lutz, E.
AU - Kessler, D. A.
AU - Barkai, E.
PY - 2011/12/9
Y1 - 2011/12/9
N2 - We derive a simple formula for the fluctuations of the time average x̄(t) around the thermal mean x eq for overdamped Brownian motion in a binding potential U(x). Using a backward Fokker-Planck equation, introduced by Szabo, Schulten, and Schulten in the context of reaction kinetics, we show that for ergodic processes these finite measurement time fluctuations are determined by the Boltzmann measure. For the widely applicable logarithmic potential, ergodicity is broken. We quantify the large nonergodic fluctuations and show how they are related to a superaging correlation function.
AB - We derive a simple formula for the fluctuations of the time average x̄(t) around the thermal mean x eq for overdamped Brownian motion in a binding potential U(x). Using a backward Fokker-Planck equation, introduced by Szabo, Schulten, and Schulten in the context of reaction kinetics, we show that for ergodic processes these finite measurement time fluctuations are determined by the Boltzmann measure. For the widely applicable logarithmic potential, ergodicity is broken. We quantify the large nonergodic fluctuations and show how they are related to a superaging correlation function.
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U2 - 10.1103/PhysRevLett.107.240603
DO - 10.1103/PhysRevLett.107.240603
M3 - Article
C2 - 22242984
AN - SCOPUS:83655191484
VL - 107
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 24
M1 - 240603
ER -