Fluctuation theorem for a deterministic one-particle system

Schmick, Malte; Markus, Mario

doi:10.1103/physreve.70.065101

Cited by 5 publications

(4 citation statements)

References 19 publications

(47 reference statements)

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“…There is a large body of computer simulation results, for various processes, that have tested the steady state fluctuation theorems, e.g. (35,36,19,27,46,47,48,49,50,51,52,53,54,55,56,57), 13 . We known of no case for which the Gallavotti-Cohen FT converges faster than the Evans-Searles FT. For temperature regulated dynamics, when the dissipative field strength is very small, the Gallavotti-Cohen FT can take extremely long times to converge.…”

Section: Gallavotti-cohen Ftmentioning

confidence: 99%

Fluctuation Theorems

Sevick

Prabhakar

Williams

et al. 2008

Annu. Rev. Phys. Chem.

255

277

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Fluctuation theorems, which have been developed over the past 15 years, have resulted in fundamental breakthroughs in our understanding of how irreversibility emerges from reversible dynamics, and have provided new statistical mechanical relationships for free energy changes. They describe the statistical fluctuations in time-averaged properties of many-particle systems such as fluids driven to nonequilibrium states, and provide some of the very few analytical expressions that describe nonequilibrium states. Quantitative predictions on fluctuations in small systems that are monitored over short periods can also be made, and therefore the arXiv:0709.3888v2 [cond-mat.stat-mech]

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Section: Gallavotti-cohen Ftmentioning

confidence: 99%

Fluctuation Theorems

Sevick

Prabhakar

Williams

et al. 2008

Annu. Rev. Phys. Chem.

255

277

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“…They show how thermodynamic irreversibility emerges from the time-reversible dynamics of the particles, and thus are of fundamental importance. The relationships also make quantitative predictions about these fluctuations, and these have been tested in computer simulations (for example see references [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]) and in laboratory experiments [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Equation ͑2͒ has been shown to apply in both the linear and nonlinear regimes to isoenergetic systems, and Eq. ͑3͒ has been shown to apply in both the linear and nonlinear regimes to a range of systems including isoenergetic, isokinetic, and Nosé-Hoover thermostatted systems, [1][2][3][4][5][6][7][8][9][10]17,19,20,34 and has recently been verified experimentally.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of the steady state fluctuation relations far from equilibrium

Williams

Searles

Evans

2006

The Journal of Chemical Physics

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Nonchaotic attractor with a highly fluctuating finite-time Lyapunov exponent in a hybrid optical system AIP Conf. Proc. 501, 342 (2000); 10.1063/1.59945Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. A thermostatted dynamical model with five degrees of freedom is used to test the fluctuation relation of Evans and Searles ͑⍀-FR͒ and that of Gallavotti and Cohen ͑⌳-FR͒. In the absence of an external driving field, the model generates a time-independent ergodic equilibrium state with two conjugate pairs of Lyapunov exponents. Each conjugate pair sums to zero. The fluctuation relations are tested numerically both near and far from equilibrium. As expected from previous work, near equilibrium the ⍀-FR is verified by the simulation data while the ⌳-FR is not confirmed by the data. Far from equilibrium where a positive exponent in one of these conjugate pairs becomes negative, we test a conjecture regarding the ⌳-FR ͓Bonetto et al., Physica D 105, 226 ͑1997͒; Giuliani et al., J. Stat. Phys. 119, 909 ͑2005͔͒. It was conjectured that when the number of nontrivial Lyapunov exponents that are positive becomes less than the number of such negative exponents, then the form of the ⌳-FR needs to be corrected. We show that there is no evidence for this conjecture in the empirical data. In fact, when the correction factor differs from unity, the corrected form of ⌳-FR is less accurate than the uncorrected ⌳-FR. Also as the field increases the uncorrected ⌳-FR appears to be satisfied with increasing accuracy. The reason for this observation is likely to be that as the field increases, the argument of the ⌳-FR more and more accurately approximates the argument of the ⍀-FR. Since the ⍀-FR works for arbitrary field strengths, the uncorrected ⌳-FR appears to become ever more accurate as the field increases. The final piece of evidence against the conjecture is that when the smallest positive exponent changes sign, the conjecture predicts a discontinuous change in the "correction factor" for ⌳-FR. We see no evidence for a discontinuity at this field strength.

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“…This process is equivalent to the system, in which the feedback controller transforms the gained information into the actual expansion work. The feedback controller system has been produced in the actual experimental study [33,34]. Thereby, let us consider the feedback controller is informed whether the signalling molecule is an active or inactive type in place of measuring the particle position.…”

Section: Szilard Engine Chain As a Brc Modelmentioning

confidence: 99%

Entropy in Cell Biology: Information Thermodynamics of a Binary Code and Szilard Engine Chain Model of Signal Transduction

Tsuruyama

2018

Entropy

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A model of signal transduction from the perspective of informational thermodynamics has been reported in recent studies, and several important achievements have been obtained. The first achievement is that signal transduction can be modelled as a binary code system, in which two forms of signalling molecules are utilised in individual steps. The second is that the average entropy production rate is consistent during the signal transduction cascade when the signal event number is maximised in the model. The third is that a Szilard engine can be a single-step model in the signal transduction. This article reviews these achievements and further introduces a new chain of Szilard engines as a biological reaction cascade (BRC) model. In conclusion, the presented model provides a way of computing the channel capacity of a BRC.

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Fluctuation theorem for a deterministic one-particle system

Cited by 5 publications

References 19 publications

Fluctuation Theorems

Fluctuation Theorems

Numerical study of the steady state fluctuation relations far from equilibrium

Entropy in Cell Biology: Information Thermodynamics of a Binary Code and Szilard Engine Chain Model of Signal Transduction

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