Role of External Flow and Frame Invariance in Stochastic Thermodynamics

Speck, Thomas; Mehl, Jakob; Seifert, Udo

doi:10.1103/physrevlett.100.178302

Cited by 59 publications

(85 citation statements)

References 30 publications

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“…This is similar to requirement of reversal of external flow direction in Ref. [42], under time reversal. The probability of time-reversed trajectory …”

Section: Equilibrium Detailed Balancesupporting

confidence: 84%

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Stochastic thermodynamics of macrospins with fluctuating amplitude and direction

2015

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We consider stochastic energy balance and entropy production (EP) in a generalized Langevin dynamics of macrospins, allowing for both amplitude and direction fluctuations, under external magnetic field. EP is calculated using Fokker-Planck equation, distinguishing between reversible and irreversible parts of probability currents. The system entropy increases due to irreversible non-equilibrium processes, and reduces as heat dissipates to surrounding environment. Using path probability distributions of time-forward trajectories and conjugate trajectories under time reversal, we obtain fluctuation theorems (FT) for total stochastic EP. We show that the choice of conjugate trajectories is crucial in obtaining entropy like quantities that obey FTs.

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“…This is similar to requirement of reversal of external flow direction in Ref. [42], under time reversal. The probability of time-reversed trajectory …”

Section: Equilibrium Detailed Balancesupporting

confidence: 84%

“…There exists various possibilities to choose conjugate trajectories under time-reversed protocol [29,42,43]. The conjugate trajectory must be carefully chosen so that the ratio P + /P − serves as a measure of irreversibility of the process, and as a result characterizes EP in the surrounding environment.…”

Section: Equilibrium Detailed Balancementioning

confidence: 99%

Stochastic thermodynamics of macrospins with fluctuating amplitude and direction

2015

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“…This fact has been discussed in ref. 23, yet the implications to single-molecule experiments have never been pointed out. Summarizing, if trap A is moved and B is at rest with respect to water, using the work W (Eq.…”

Section: The Modelmentioning

confidence: 99%

Free-energy inference from partial work measurements in small systems

Ribezzi-Crivellari¹,

Ritort²

2014

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

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Fluctuation relations (FRs) are among the few existing general results in nonequilibrium systems. Their verification requires the measurement of the total work performed on a system. Nevertheless in many cases only a partial measurement of the work is possible. Here we consider FRs in dual-trap optical tweezers where two different forces (one per trap) are measured. With this setup we perform pulling experiments on single molecules by moving one trap relative to the other. We demonstrate that work should be measured using the force exerted by the trap that is moved. The force that is measured in the trap at rest fails to provide the full dissipation in the system, leading to a (incorrect) work definition that does not satisfy the FR. The implications to single-molecule experiments and free-energy measurements are discussed. In the case of symmetric setups a second work definition, based on differential force measurements, is introduced. This definition is best suited to measure free energies as it shows faster convergence of estimators. We discuss measurements using the (incorrect) work definition as an example of partial work measurement. We show how to infer the full work distribution from the partial one via the FR. The inference process does also yield quantitative information, e.g., the hydrodynamic drag on the dumbbell. Results are also obtained for asymmetric dualtrap setups. We suggest that this kind of inference could represent a previously unidentified and general application of FRs to extract information about irreversible processes in small systems.statistical mechanics | biophysics | fluctuation theorems F luctuation relations (FRs) are mathematical equations connecting non equilibrium work measurements to equilibrium free-energy differences. FRs, such as the Jarzynski equality (JE) or the Crooks fluctuation relation (CFR), have become a valuable tool in single-molecule biophysics where they are used to measure folding free energies from irreversible pulling experiments (1, 2). Such measurements have been carried out with laser optical tweezers on different nucleic acid structures such as hairpins (3-6), G quadruplexes (7,8), and proteins (9-12) and with atomic force microscopes on proteins (13) and bimolecular complexes (14). An important issue regarding FRs is the correct definition of work, which rests on the correct identification of configurational variables and control parameters. In the singletrap optical tweezers configuration this issue has been thoroughly discussed (17)(18)(19).The situation of how to correctly measure work in small systems becomes subtle when there are different forces applied to the system. In this case theory gives the prescription to correctly define the work (W Γ ) for a given trajectory (Γ): Integrate the generalized force (f λ ) (conjugated to the control parameter, λ) over λ along Γ, W Γ = R Γ f λ dλ. However, in some cases one cannot measure the proper generalized force or has limited experimental access to partial sources of the entropy production, leading to wha...

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“…This fact has been discussed in literature and questions have been posed as to which choice would be physically meaningful [12,61,62]. For example, consider entropy production in soft matter system in external shear flow [61,62].…”

Section: Fluctuation Theoremsmentioning

confidence: 99%

Macrospin in external magnetic field: entropy production and fluctuation theorems

2015

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We consider stochastic rotational dynamics of a macrospin at a constant temperature, in presence of an external magnetic field. Starting from the appropriate Langevin equation which contains multiplicative noise, we calculate entropy production (EP) along stochastic trajectories, and obtain fluctuation theorems. The system remains inherently out of equilibrium due to a spin torque supporting azimuthal current, leading to an excess EP apart from the EP due to heat dissipation. The anomaly may be removed using a redefinition of dissipated heat and stochastic work done. Using numerical simulations, we obtain distribution functions for entropy production along stochastic trajectories to find good agreement with the detailed fluctuation theorem.

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Role of External Flow and Frame Invariance in Stochastic Thermodynamics

Cited by 59 publications

References 30 publications

Stochastic thermodynamics of macrospins with fluctuating amplitude and direction

Stochastic thermodynamics of macrospins with fluctuating amplitude and direction

Free-energy inference from partial work measurements in small systems

Macrospin in external magnetic field: entropy production and fluctuation theorems

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