1,304 research outputs found

    Effective thermodynamics for a marginal observer

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    Thermodynamics is usually formulated on the presumption that the observer has complete information about the system he/she deals with: no parasitic current, exact evaluation of the forces that drive the system. For example, the acclaimed Fluctuation Relation (FR), relating the probability of time-forward and time-reversed trajectories, assumes that the measurable transitions suffice to characterize the process as Markovian (in our case, a continuous-time jump process). However, most often the observer only measures a marginal current. We show that he/she will nonetheless produce an effective description that does not dispense with the fundamentals of thermodynamics, including the FR and the 2nd law. Our results stand on the mathematical construction of a hidden time reversal of the dynamics, and on the physical requirement that the observed current only accounts for a single transition in the configuration space of the system. We employ a simple abstract example to illustrate our results and to discuss the feasibility of generalizations.Comment: 8 pages, 1 figur

    Transient fluctuation theorems for the currents and initial equilibrium ensembles

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    We prove a transient fluctuation theorem for the currents for continuous-time Markov jump processes with stationary rates, generalizing an asymptotic result by Andrieux and Gaspard [J. Stat. Phys. 127, 107 (2007)] to finite times. The result is based on a graph theoretical decomposition in cycle currents and an additional set of tidal currents that characterize the transient relaxation regime. The tidal term can then be removed by a preferred choice of a suitable initial equilibrium ensemble, a result that provides the general theory for the fluctuation theorem without ensemble quantities recently addressed in [Phys. Rev. E 89, 052119 (2014)]. As an example we study the reaction network of a simple stochastic chemical engine, and finally we digress on general properties of fluctuation relations for more complex chemical reaction networks.Comment: 19 pages, 2 figures. Sign error corrected in Eq.(50) and followin

    Tightening the uncertainty principle for stochastic currents

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    We connect two recent advances in the stochastic analysis of nonequilibrium systems: the (loose) uncertainty principle for the currents, which states that statistical errors are bounded by thermodynamic dissipation; and the analysis of thermodynamic consistency of the currents in the light of symmetries. Employing the large deviation techniques presented in [Gingrich et al., Phys. Rev. Lett. 2016] and [Pietzonka et al., Phys. Rev. E 2016], we provide a short proof of the loose uncertainty principle, and prove a tighter uncertainty relation for a class of thermodynamically consistent currents JJ. Our bound involves a measure of partial entropy production, that we interpret as the least amount of entropy that a system sustaining current JJ can possibly produce, at a given steady state. We provide a complete mathematical discussion of quadratic bounds which allows to determine which are optimal, and finally we argue that the relationship for the Fano factor of the entropy production rate varσ/meanσ2\mathrm{var}\, \sigma / \mathrm{mean}\, \sigma \geq 2 is the most significant realization of the loose bound. We base our analysis both on the formalism of diffusions, and of Markov jump processes in the light of Schnakenberg's cycle analysis.Comment: 13 pages, 4 figure

    Dissipation in noisy chemical networks: The role of deficiency

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    We study the effect of intrinsic noise on the thermodynamic balance of complex chemical networks subtending cellular metabolism and gene regulation. A topological network property called deficiency, known to determine the possibility of complex behavior such as multistability and oscillations, is shown to also characterize the entropic balance. In particular, only when deficiency is zero does the average stochastic dissipation rate equal that of the corresponding deterministic model, where correlations are disregarded. In fact, dissipation can be reduced by the effect of noise, as occurs in a toy model of metabolism that we employ to illustrate our findings. This phenomenon highlights that there is a close interplay between deficiency and the activation of new dissipative pathways at low molecule numbers.Comment: 10 Pages, 6 figure

    Efficiency statistics at all times: Carnot limit at finite power

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    We derive the statistics of the efficiency under the assumption that thermodynamic fluxes fluctuate with normal law, parametrizing it in terms of time, macroscopic efficiency, and a coupling parameter ζ\zeta. It has a peculiar behavior: No moments, one sub- and one super-Carnot maxima corresponding to reverse operating regimes (engine/pump), the most probable efficiency decreasing in time. The limit ζ0\zeta\to 0 where the Carnot bound can be saturated gives rise to two extreme situations, one where the machine works at its macroscopic efficiency, with Carnot limit corresponding to no entropy production, and one where for a transient time scaling like 1/ζ1/\zeta microscopic fluctuations are enhanced in such a way that the most probable efficiency approaches Carnot at finite entropy production.Comment: 5+4 pages, 4 figures. Title modifie

    Effective fluctuation and response theory

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    The response of thermodynamic systems perturbed out of an equilibrium steady-state is described by the reciprocal and the fluctuation-dissipation relations. The so-called fluctuation theorems extended the study of fluctuations far beyond equilibrium. All these results rely on the crucial assumption that the observer has complete information about the system. Such a precise control is difficult to attain, hence the following questions are compelling: Will an observer who has marginal information be able to perform an effective thermodynamic analysis? Given that such observer will only establish local equilibrium amidst the whirling of hidden degrees of freedom, by perturbing the stalling currents will he/she observe equilibrium-like fluctuations? We model the dynamics of open systems as Markov jump processes on finite networks. We establish that: 1) While marginal currents do not obey a full-fledged fluctuation relation, there exist effective affinities for which an integral fluctuation relation holds; 2) Under reasonable assumptions on the parametrization of the rates, effective and "real" affinities only differ by a constant; 3) At stalling, i.e. where the marginal currents vanish, a symmetrized fluctuation-dissipation relation holds while reciprocity does not; 4) There exists a notion of marginal time-reversal that plays a role akin to that played by time-reversal for complete systems, which restores the fluctuation relation and reciprocity. The above results hold for configuration-space currents, and for phenomenological currents provided that certain symmetries of the effective affinities are respected - a condition whose range of validity we deem the most interesting question left open to future inquiry. Our results are constructive and operational: we provide an explicit expression for the effective affinities and propose a procedure to measure them in laboratory.Comment: 41 pages. Comments are welcome

    Multicyclic Norias: A First-Transition Approach to Extreme Values of the Currents

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    For continuous-time Markov chains we prove that, depending on the notion of effective affinity F, the probability of an edge current to ever become negative is either 1 if F&lt;0 else ∼exp-F. The result generalizes a “noria” formula to multicyclic networks. We give operational insights on the effective affinity and compare several estimators, arguing that stopping problems may be more accurate in assessing the nonequilibrium nature of a system according to a local observer. Finally we elaborate on the similarity with the Boltzmann formula. The results are based on a constructive first-transition approach.</p
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