Experimental test of Hatano and Sasa's nonequilibrium steady-state equality

Trepagnier, Eliane; Jarzynski, Christopher; Ritort, Fèlix; Crooks, Gavin E.; Bustamante, Carlos; Liphardt, Jan

doi:10.1073/pnas.0406405101

Cited by 242 publications

(245 citation statements)

References 27 publications

Supporting

Mentioning

236

Contrasting

Unclassified

Order By: Relevance

“…These results include entropy production theorems [2], Jarzynski equality [3], Crooks relations [4], Hatano-Sasa identity [5], etc. Some of the above relations have been verified experimentally on single nanosize systems in physical envirnoments where fluctuations play a dominant role [6,7].…”

mentioning

confidence: 86%

“…Work distributions have been calculated analytically for several model systems and tested against various fluctuation theorems [9][10][11]. JE has been generalized to arbitrary transitions between nonequilibrium steady states by Hatano and Sasa [5], which has also been verified experimentally [7]. In our present work, we determine the work distributions analytically for two different models.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Charged particle in a magnetic field: Jarzynski equality

Jayannavar

Sahoo

2007

Phys. Rev. E

View full text Add to dashboard Cite

We describe some solvable models which illustrate the Jarzynski theorem and related fluctuation theorems. We consider a charged particle in the presence of magnetic field in a two dimensional harmonic well. In the first case the centre of the harmonic potential is translated with a uniform velocity, while in the other case the particle is subjected to an ac force. We show that Jarzynski identity complements Bohr-van Leeuwen theorem on the absence of diamagnetism in equilibrium classical system. PACS numbers: 05.70. Ln, 05.40. a, 05.40.Jc Most processes that occur in nature are far from equilibrium and hence cannot be treated within the framework of classical thermodynamics. The traditional nonequilibrium statistical mechanics deals with systems near equilibrium in the linear response regime. Its success has lead to the formulation of fluctuation-dissipation relation, Onsagar's reciprocity relations and the KuboGreen formulae, etc. However, very recent developments in nonequilibrium statistical mechanics have resulted in the discovery of some exact theoretical results for systems driven far away from equilibrium and are collectively called fluctuation theorems [1]. These results include entropy production theorems The concept of free energy is of central importance in statistical mechanics and thermodynamics. With the help of free energy one can calculate all the phases of a system and their physical properties. However, the free energy of the system relative to an arbitrary reference state is often difficult to determine. Jarzynski equality(JE) relates non-equilibrium quantities with equilibrium free energies [3]. In this prescription, initially the system is assumed to be in equilibrium state determined by a thermodynamic parameter A defined by a control parameter λ A and is kept in contact with a heat bath at temperature T. The nonequilibrium process is obtained by changing the thermodynamic control parameter λ in a finite time τ according to a prescribed protocol λ(t), from λ A = λ(t=0) to some final value λ B = λ(t = τ ). The final state of the system at time τ (at the end of the protocol) will in general not be at equilibrium. It will equilibrate to a final state B(≡ λ B ) if it is further allowed to evolve by keeping parameter λ B fixed. JE states thatWhere ∆F is the free energy difference between equilibrium states A and B. Angular bracket ... denotes the average taken over different realizations for fixed protocol λ(t). W is work expended during each repetation of the protocol and is a realization dependent random variable. Jarzynski's theorem has been derived using various methods with different system dynamics [3][4][5]8]. This remarkable identity provides a practical tool to determine equilibrium thermodynamic potentials from processes carried out arbitrarily far away from equilibrium. This identity has been used to extract equilibrium free energy differences in experiments. Work distributions have been calculated analytically for several model systems and tested against various fluctuati...

show abstract

mentioning

confidence: 86%

mentioning

confidence: 99%

Charged particle in a magnetic field: Jarzynski equality

Jayannavar

Sahoo

2007

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…14 Their result was tested and confirmed last year by a measurement of the dissipation and fluctuations of microspheres optically driven through water. 15 Those theoretical and experimental advances represent steps toward a complete theory of steady-state thermodynamics. Such a theory would have a profound effect on how scientists describe nonequilibrium steady-state systems such as molecular machines and cells.…”

Section: Experimental Tests Of Fluctuation Theoremsmentioning

confidence: 99%

The Nonequilibrium Thermodynamics of Small Systems

2005

View full text Add to dashboard Cite

show abstract

“…They therefore quantify the statistical significance of nonthermodynamic behaviors which can become significant in small systems [18,19]. Various experimental verifications of these FTs have been reported [20,21,22,23,24,25,26]. In this paper, we consider an open system, described by a master equation (ME), exchanging matter and energy with multiple reservoirs.…”

Section: Introductionmentioning

confidence: 99%

Entropy fluctuation theorems in driven open systems: Application to electron counting statistics

2007

View full text Add to dashboard Cite

The total entropy production generated by the dynamics of an externally driven systems exchanging energy and matter with multiple reservoirs and described by a master equation is expressed as the sum of three contributions, each corresponding to a distinct mechanism for bringing the system out of equilibrium: nonequilibrium initial conditions, external driving, and breaking of detailed balance. We derive three integral fluctuation theorems (FTs) for these contributions and show that they lead to the following universal inequality: an arbitrary nonequilibrium transformation always produces a change in the total entropy production greater or equal than the one produced if the transformation is done very slowly (adiabatically). Previously derived fluctuation theorems can be recovered as special cases. We show how these FTs can be experimentally tested by performing the counting statistics of the electrons crossing a single level quantum dot coupled to two reservoirs with externally varying chemical potentials. The entropy probability distributions are simulated for driving protocols ranging from the adiabatic to the sudden switching limit.

show abstract

Experimental test of Hatano and Sasa's nonequilibrium steady-state equality

Cited by 242 publications

References 27 publications

Charged particle in a magnetic field: Jarzynski equality

Charged particle in a magnetic field: Jarzynski equality

The Nonequilibrium Thermodynamics of Small Systems

Entropy fluctuation theorems in driven open systems: Application to electron counting statistics

Contact Info

Product

Resources

About