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The stochastic thermodynamics of a rotating Brownian particle in a gradient flow.

Lan Y, Aurell E - Sci Rep (2015)

Bottom Line: We compute the entropy production engendered in the environment from a single Brownian particle which moves in a gradient flow, and show that it corresponds in expectation to classical near-equilibrium entropy production in the surrounding fluid with specific mesoscopic transport coefficients.With temperature gradient, extra terms are found which result from the nonlinear interaction between the particle and the non-equilibrated environment.The calculations are based on the fluctuation relations which relate entropy production to the probabilities of stochastic paths and carried out in a multi-time formalism.

View Article: PubMed Central - PubMed

Affiliation: 1] The Department of Physics Tsinghua University, 100084 Beijing, China [2] Collaborative Innovation Center of Quantum Matter, Beijing 100084, China.

ABSTRACT
We compute the entropy production engendered in the environment from a single Brownian particle which moves in a gradient flow, and show that it corresponds in expectation to classical near-equilibrium entropy production in the surrounding fluid with specific mesoscopic transport coefficients. With temperature gradient, extra terms are found which result from the nonlinear interaction between the particle and the non-equilibrated environment. The calculations are based on the fluctuation relations which relate entropy production to the probabilities of stochastic paths and carried out in a multi-time formalism.

No MeSH data available.


Related in: MedlinePlus

Entropy production of one Brownian particle in a gradient flow.(a) a ring setup for generating the gradient flow and the temperature field, (b) entropy contribution of different terms of Eq. (13) with increasing outer radius, coming from different sources: purely flow gradient contribution  (cross) from the first term of Eq. (13); the rest two terms contributed by Squad representing the temperature field coupled with the translation (dashed line) indicated by γ, the temperature field coupled with the rotation (dot-dashed line) indicated by γ2. Three contributions combined are depicted by the solid line.
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f1: Entropy production of one Brownian particle in a gradient flow.(a) a ring setup for generating the gradient flow and the temperature field, (b) entropy contribution of different terms of Eq. (13) with increasing outer radius, coming from different sources: purely flow gradient contribution (cross) from the first term of Eq. (13); the rest two terms contributed by Squad representing the temperature field coupled with the translation (dashed line) indicated by γ, the temperature field coupled with the rotation (dot-dashed line) indicated by γ2. Three contributions combined are depicted by the solid line.

Mentions: In Fig. 1(a), a simple experimental setup is depicted which may be used to measure entropy production of Brownian particles in a gradient flow with temperature variation. The whole setup is rotationally symmetric with the inner radius R1 = 500 μm and the outer radius R2 = 1000 μm. Below, we use dimensionless quantities to represent our physical variables (See the previous discussion about scales of various variables. A more detailed explanation is included in the Supplementary Information.). For example, the radius of the particle is 1 which is used as the length scale and is 1 μm physically. The time scale is taken to be tu ~ 10−3 s. With this convention, in water, the rescaled translational friction coefficient is γ = 4.53 × 103 and the rotational one γ2 = 1.51 × 104. The flow is incompressible and irrotational with a profile and temperature T = 1/(k2r + t2), where k1 = 2000 and k2 = 1/2000, t2 = 0.5. With this setup, Eq. (12) gives


The stochastic thermodynamics of a rotating Brownian particle in a gradient flow.

Lan Y, Aurell E - Sci Rep (2015)

Entropy production of one Brownian particle in a gradient flow.(a) a ring setup for generating the gradient flow and the temperature field, (b) entropy contribution of different terms of Eq. (13) with increasing outer radius, coming from different sources: purely flow gradient contribution  (cross) from the first term of Eq. (13); the rest two terms contributed by Squad representing the temperature field coupled with the translation (dashed line) indicated by γ, the temperature field coupled with the rotation (dot-dashed line) indicated by γ2. Three contributions combined are depicted by the solid line.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4508657&req=5

f1: Entropy production of one Brownian particle in a gradient flow.(a) a ring setup for generating the gradient flow and the temperature field, (b) entropy contribution of different terms of Eq. (13) with increasing outer radius, coming from different sources: purely flow gradient contribution (cross) from the first term of Eq. (13); the rest two terms contributed by Squad representing the temperature field coupled with the translation (dashed line) indicated by γ, the temperature field coupled with the rotation (dot-dashed line) indicated by γ2. Three contributions combined are depicted by the solid line.
Mentions: In Fig. 1(a), a simple experimental setup is depicted which may be used to measure entropy production of Brownian particles in a gradient flow with temperature variation. The whole setup is rotationally symmetric with the inner radius R1 = 500 μm and the outer radius R2 = 1000 μm. Below, we use dimensionless quantities to represent our physical variables (See the previous discussion about scales of various variables. A more detailed explanation is included in the Supplementary Information.). For example, the radius of the particle is 1 which is used as the length scale and is 1 μm physically. The time scale is taken to be tu ~ 10−3 s. With this convention, in water, the rescaled translational friction coefficient is γ = 4.53 × 103 and the rotational one γ2 = 1.51 × 104. The flow is incompressible and irrotational with a profile and temperature T = 1/(k2r + t2), where k1 = 2000 and k2 = 1/2000, t2 = 0.5. With this setup, Eq. (12) gives

Bottom Line: We compute the entropy production engendered in the environment from a single Brownian particle which moves in a gradient flow, and show that it corresponds in expectation to classical near-equilibrium entropy production in the surrounding fluid with specific mesoscopic transport coefficients.With temperature gradient, extra terms are found which result from the nonlinear interaction between the particle and the non-equilibrated environment.The calculations are based on the fluctuation relations which relate entropy production to the probabilities of stochastic paths and carried out in a multi-time formalism.

View Article: PubMed Central - PubMed

Affiliation: 1] The Department of Physics Tsinghua University, 100084 Beijing, China [2] Collaborative Innovation Center of Quantum Matter, Beijing 100084, China.

ABSTRACT
We compute the entropy production engendered in the environment from a single Brownian particle which moves in a gradient flow, and show that it corresponds in expectation to classical near-equilibrium entropy production in the surrounding fluid with specific mesoscopic transport coefficients. With temperature gradient, extra terms are found which result from the nonlinear interaction between the particle and the non-equilibrated environment. The calculations are based on the fluctuation relations which relate entropy production to the probabilities of stochastic paths and carried out in a multi-time formalism.

No MeSH data available.


Related in: MedlinePlus