Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics

Bochkov, G. N.; Kuzovlev, Yu. E.

doi:10.1016/0378-4371(81)90122-9

Cited by 240 publications

(383 citation statements)

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“…[41] Thus, one has to be quite careful when defining the external work, as that choice can substantially change the final form for any fluctuation relation [9]. Indeed, fluctuation relations that are derived under distinct choices of the definition of work used will lead to distinct forms of the fluctuation theorems [8,9,[11][12][13][14][15][16][17][18][19][20] (FT). The JE have been demonstrated exactly for systems initially thermalized at temperature T , that can be either mechanically closed or in contact with a thermostat (at temperature T also) all the time.…”

Section: Introductionmentioning

confidence: 99%

Exact nonequilibrium work generating function for a small classical system

Morgado¹,

Soares-Pinto

2010

Phys. Rev. E

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We obtain the exact nonequilibrium work generating function (NEWGF), for a small system consisting of a massive Brownian particle connected to internal and external springs. The external work is provided to the system for a finite time interval. The Jarzynski equality (JE), obtained in this case directly from the NEWGF, is shown to be valid for the present model, in an exact way regardless of the rate of external work.

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Section: Introductionmentioning

confidence: 99%

Exact nonequilibrium work generating function for a small classical system

Morgado¹,

Soares-Pinto

2010

Phys. Rev. E

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“…This equilibrium-like behavior perhaps can be understood in the context of a generalized f luctuation dissipation theorem (12),…”

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confidence: 98%

“…The striking relation ͗exp(Ϫ⌬E/k B T)͘ ϭ 1 for the change in internal energy averaged over many trajectories follows immediately from Eq. 2 (12).…”

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confidence: 99%

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Coupled transport at the nanoscale: The unreasonable effectiveness of equilibrium theory

Astumian

2007

Proc. Natl. Acad. Sci. U.S.A.

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T he Soret effect, also known as thermodiffusion, is a classic example of coupled transport (1) in which directed motion of a particle or macromolecule is driven by f low of heat down a thermal gradient. Generally, a particle moves from hot to cold, but the reverse is also seen under some conditions. Although it has been known for Ͼ150 years, the microscopic explanation of the Soret effect has remained unclear. In a recent issue of PNAS, Duhr and Braun (2) shed important light on the molecular mechanisms of the Soret effect by using a technique of singleparticle tracking, which allows very sensitive measurements of how thermodiffusion can be inf luenced by changes in the environment, as well as how the effect scales with parameters such as particle size and surface charge. Although there are numerous examples (3, 4) of exciting possibilities for technological uses of thermodiffusion, the importance of understanding the mechanism of the Soret effect goes beyond the practical applications. Ultimately, similar coupled processes in which a chemical reaction drives directed motion of a protein may lie at the heart of the mechanism of the biological motors and pumps essential for life. Detailed understanding of a variety of coupled transport processes, including the Soret effect, may lead to important advances in our ability to inf luence biological molecules and to use the insight gained from natural systems to help design synthetic nanoscale machines.The Soret effect can be characterized in terms of two parameters: the thermal diffusion coefficient D T , defined by the assumed linear relationship between the velocity and the thermal gradient v ϭ ϪD T ٌT, and the Soret coefficient, S T ϭ D T /D, which is the ratio between D T and the scalar diffusion coefficient D. To unravel the molecular mechanism for thermodiffusion, it is essential to understand how the parameters D T and S T depend on the properties of the solvent and solute (or colloidal particles) and to determine the general mechanisms by which particles move along a thermal gradient.There are two generic classes of mechanisms by which thermodiffusion can occur: one based on f luid dynamics and the other based on thermodynamics. In the class based on hydrodynamics (5), the temperature gradient leads directly to some imbalance over the surface of the molecule that results in a net mechanical force F that drives the particle motion. A similar mechanism, although not involving a thermal gradient, has been proposed as a description of a selfpropelled molecular motor driven by a chemical reaction catalyzed by the motor that creates an osmotic gradient that pushes the motor along (6). In the second type of mechanism, the local thermodynamic environment of the particle is effectively isotropic (7). The chemical potential of the particle depends on temperature and hence on space, but gently, in comparison with the radius of the particle itself. The particle moves preferentially to the colder regions, in which it is thermodynamically more stable, by random diffusion t...

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“…An important achievement in the field is the discovery of new fluctuation theorems, which generalize the Clausius identity in giving the exact mean value of the exponential of the work. This Jarzynski identity (Bochkov & Kuzovlev, 1981a;b;Evans et al, 1993;Gallavotti & Cohen, 1995;Jarzynski, 1997b;a;Crooks, 1998;2000;Maes, 2004;Hatano & Sasa, 2001;Speck & Seifert, 2004;Seifert, 2005;Schuler et al, 2005;Esposito & Mukamel, 2006;Hänggi & Thomas, 1975) enables one to specify the free energy difference between two equilibrium states. This is done by repeating real time (i.e.…”

Section: Introductionmentioning

confidence: 99%