TY - JOUR

T1 - Physical insight into the thermodynamic uncertainty relation using Brownian motion in tilted periodic potentials

AU - Hyeon, Changbong

AU - Hwang, Wonseok

N1 - Publisher Copyright:
© 2017 American Physical Society.

PY - 2017/7/31

Y1 - 2017/7/31

N2 - Using Brownian motion in periodic potentials V(x) tilted by a force f, we provide physical insight into the thermodynamic uncertainty relation, a recently conjectured principle for statistical errors and irreversible heat dissipation in nonequilibrium steady states. According to the relation, nonequilibrium output generated from dissipative processes necessarily incurs an energetic cost or heat dissipation q, and in order to limit the output fluctuation within a relative uncertainty ϵ, at least 2kBT/ϵ2 of heat must be dissipated. Our model shows that this bound is attained not only at near-equilibrium [f V′(x)] but also at far-from-equilibrium [f V′(x)], more generally when the dissipated heat is normally distributed. Furthermore, the energetic cost is maximized near the critical force when the barrier separating the potential wells is about to vanish and the fluctuation of Brownian particles is maximized. These findings indicate that the deviation of heat distribution from Gaussianity gives rise to the inequality of the uncertainty relation, further clarifying the meaning of the uncertainty relation. Our derivation of the uncertainty relation also recognizes a bound of nonequilibrium fluctuations that the variance of dissipated heat (σq2) increases with its mean (μq), and it cannot be smaller than 2kBTμq.

AB - Using Brownian motion in periodic potentials V(x) tilted by a force f, we provide physical insight into the thermodynamic uncertainty relation, a recently conjectured principle for statistical errors and irreversible heat dissipation in nonequilibrium steady states. According to the relation, nonequilibrium output generated from dissipative processes necessarily incurs an energetic cost or heat dissipation q, and in order to limit the output fluctuation within a relative uncertainty ϵ, at least 2kBT/ϵ2 of heat must be dissipated. Our model shows that this bound is attained not only at near-equilibrium [f V′(x)] but also at far-from-equilibrium [f V′(x)], more generally when the dissipated heat is normally distributed. Furthermore, the energetic cost is maximized near the critical force when the barrier separating the potential wells is about to vanish and the fluctuation of Brownian particles is maximized. These findings indicate that the deviation of heat distribution from Gaussianity gives rise to the inequality of the uncertainty relation, further clarifying the meaning of the uncertainty relation. Our derivation of the uncertainty relation also recognizes a bound of nonequilibrium fluctuations that the variance of dissipated heat (σq2) increases with its mean (μq), and it cannot be smaller than 2kBTμq.

UR - http://www.scopus.com/inward/record.url?scp=85027025527&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.96.012156

DO - 10.1103/PhysRevE.96.012156

M3 - Article

C2 - 29347275

AN - SCOPUS:85027025527

SN - 2470-0045

VL - 96

JO - Physical Review E

JF - Physical Review E

IS - 1

M1 - 012156

ER -