Equality Connecting Energy Dissipation with a Violation of the Fluctuation-Response Relation

Harada, Takahiro; Sasa, Shigehiko

doi:10.1103/physrevlett.95.130602

Cited by 328 publications

(392 citation statements)

References 24 publications

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“…Formal treatments of fluctuationresponse in periodically forced systems by Teramoto, Harada, and Sasa 74,75 provide insight into the rate of energy dissipation in such systems. Green et al 76 have shown that the rate of energy dissipation is directly related to the dynamical entropy of the system.…”

Section: Characterizing Noisy Reactions With the Noise-free Geometrymentioning

confidence: 99%

Chemical reactions induced by oscillating external fields in weak thermal environments

Craven

Bartsch

Hernandez

2015

The Journal of Chemical Physics

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Chemical reaction rates must increasingly be determined in systems that evolve under the control of external stimuli. In these systems, when a reactant population is induced to cross an energy barrier through forcing from a temporally varying external field, the transition state that the reaction must pass through during the transformation from reactant to product is no longer a fixed geometric structure, but is instead timedependent. For a periodically forced model reaction, we develop a recrossing-free dividing surface that is attached to a transition state trajectory [T. Bartsch, R. Hernandez, and T. Uzer, Phys. Rev. Lett. 95, 058301 (2005)]. We have previously shown that for single-mode sinusoidal driving, the stability of the timevarying transition state directly determines the reaction rate [G. T. Craven, T. Bartsch, and R. Hernandez, J. Chem. Phys. 141, 041106 (2014)]. Here, we extend our previous work to the case of multi-mode driving waveforms. Excellent agreement is observed between the rates predicted by stability analysis and rates obtained through numerical calculation of the reactive flux. We also show that the optimal dividing surface and the resulting reaction rate for a reactive system driven by weak thermal noise can be approximated well using the transition state geometry of the underlying deterministic system. This agreement persists as long as the thermal driving strength is less than the order of that of the periodic driving. The power of this result is its simplicity. The surprising accuracy of the time-dependent noise-free geometry for obtaining transition state theory rates in chemical reactions driven by periodic fields reveals the dynamics without requiring the cost of brute-force calculations.

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Section: Characterizing Noisy Reactions With the Noise-free Geometrymentioning

confidence: 99%

Chemical reactions induced by oscillating external fields in weak thermal environments

Craven

Bartsch

Hernandez

2015

The Journal of Chemical Physics

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“…The expression in Eq. (24) suggests that the it might be related to the violation of the fluctuation dissipation relation in the NESS [26][27][28]. It should be scrutinized further in future.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…It has been shown that the special choice of f c = −T ∇ x φ ss guarantees Eq. (26). One may ask whether the converse is also true.…”

Section: Nonconservative Force Casementioning

confidence: 99%

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Stochastic echo phenomena in nonequilibrium systems

Noh

2014

Journal of the Korean Physical Society

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A thermodynamic system is driven out of equilibrium by a time-dependent force or a nonconservative force represented with a protocol λ(t). Dynamics of such a system is irreversible so that the ensemble of trajectories under a time-reversed protocol λ(−t) is not equivalent to that of timereversed trajectories under λ(t). We raise a question whether one can find a suitable protocol under which the system exhibits time-reversed motions of the original system. Such a phenomenon is referred to as a stochastic echo phenomenon. We derive a condition for the optimal protocol that leads to the stochastic echo phenomenon in Langevin systems. We find that any system driven by timeindependent nonconservative forces has a dual system exhibiting the stochastic echo phenomenon perfectly. The stochastic echo phenomena are also demonstrated for harmonic oscillator systems driven by time-dependent forces. Our study provides a novel perspective on the time-irreversibility of nonequilibrium systems.

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“…In previous work, e.g. [2,8,17] about nonequilibrium linear response, while in the same spirit, the nonequilibrium dynamics was not explicitly time-dependent. We need these new formulae (derived in the Appendix) however for the application described in this paper.…”

Section: Linear Response Around Time-dependent Nonequilibriamentioning

confidence: 99%

Friction and noise for a probe in a nonequilibrium fluid

Maes

Steffenoni

2015

Phys. Rev. E

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Abstract. We investigate the fluctuation dynamics of a probe around a deterministic motion induced by interactions with driven particles. The latter constitute the nonequilibrium medium in which the probe is immersed and is modelled as overdamped Langevin particle dynamics driven by nonconservative forces. The expansion that yields the friction and noise expressions for the reduced probe dynamics is based on linear response around a time-dependent nonequilibrium condition of the medium. The result contains an extension of the second fluctuation-dissipation relation between friction and noise for probe motion in a nonequilibrium fluid. The problemWhether the environment of a system is in equilibrium or is driven into a nonequilibrium condition is important for characterizing internal motions and reactions. In other words the reduced system dynamics will reflect whether the environment is driven or not.For example, the relation between noise and friction on the system need no longer be described via the standard second fluctuation-dissipation (or Einstein) relation, we cannot unambiguously speak about entropy fluxes into the environment in terms of heat as there would be no Clausius relation, and system fluctuations or noise level in general are not simply quantified by a reservoir temperature. The present paper takes up the challenge of characterizing such an effective dynamics for a probe in contact with a nonequilibrium medium. One should have in mind that the medium consists of active elements or driven particles themselves in contact with a big thermal equilibrium reservoir (like surrounding air or water). Combined, the medium and the heat bath make up the nonequilibrium fluid. The system is called a probe here, but it can in general also refer to a collective or with j = 1, . . . , N labeling the particles and subject to independent standard white noises ξ j t . The β denotes the inverse temperature of the background equilibrium reservoir but the particles are effectively driven by the nonconservative force F . For simplicity we have not introduced explicitly friction and mass parameters, keeping only λ (coupling) and β as parameters. The particle interaction is given through the potential Φ while the potential U depends on the position X t of the probe, thus representing the back-reaction of the probe on each particle. Other and different types of interaction between probe and medium are possible, e.g. in terms of their center of mass coordinate with a mean field type potential U ( j x j t − X t ), here not discussed and inessential for the present level of discussion. Keeping to (1.1) the probe dynamics itself iswhere we indicate by K X t ,Ẋ t other aspects of the probe motion in the fluid. Its mass M is obviously also an important parameter for separation of time-scales between probe and fluid particle motion.The equations (1.1) and (1.2) starting at t = 0 are the basic evolution equations representing the coupled dynamics of probe and fluid particles. Nonequilibrium works directly on the medium which is ...

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Equality Connecting Energy Dissipation with a Violation of the Fluctuation-Response Relation

Cited by 328 publications

References 24 publications

Chemical reactions induced by oscillating external fields in weak thermal environments

Chemical reactions induced by oscillating external fields in weak thermal environments

Stochastic echo phenomena in nonequilibrium systems

Friction and noise for a probe in a nonequilibrium fluid

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