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See detailFluctuating currents in stochastic thermodynamics. II. Energy conversion and nonequilibrium response in kinesin models
Altaner, Bernhard; Wachtel, Artur UL; Vollmer, Jürgen

in PHYSICAL REVIEW E (2015), 92(4), 042133

Unlike macroscopic engines, the molecular machinery of living cells is strongly affected by fluctuations. Stochastic thermodynamics uses Markovian jump processes to model the random transitions between ... [more ▼]

Unlike macroscopic engines, the molecular machinery of living cells is strongly affected by fluctuations. Stochastic thermodynamics uses Markovian jump processes to model the random transitions between the chemical and configurational states of these biological macromolecules. A recently developed theoretical framework [A. Wachtel, J. Vollmer, and B. Altaner, Phys. Rev. E 92, 042132 (2015)] provides a simple algorithm for the determination of macroscopic currents and correlation integrals of arbitrary fluctuating currents. Here we use it to discuss energy conversion and nonequilibrium response in different models for the molecular motor kinesin. Methodologically, our results demonstrate the effectiveness of the algorithm in dealing with parameter-dependent stochastic models. For the concrete biophysical problem our results reveal two interesting features in experimentally accessible parameter regions: the validity of a nonequilibrium Green-Kubo relation at mechanical stalling as well as a negative differential mobility for superstalling forces. [less ▲]

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See detailFluctuating currents in stochastic thermodynamics. I. Gauge invariance of asymptotic statistics
Wachtel, Artur UL; Vollmer, Jürgen; Altaner, Bernhard

in PHYSICAL REVIEW E (2015), 92(4), 042132

Stochastic thermodynamics uses Markovian jump processes to model random transitions between observable mesoscopic states. Physical currents are obtained from antisymmetric jump observables defined on the ... [more ▼]

Stochastic thermodynamics uses Markovian jump processes to model random transitions between observable mesoscopic states. Physical currents are obtained from antisymmetric jump observables defined on the edges of the graph representing the network of states. The asymptotic statistics of such currents are characterized by scaled cumulants. In the present work, we use the algebraic and topological structure of Markovian models to prove a gauge invariance of the scaled cumulant-generating function. Exploiting this invariance yields an efficient algorithm for practical calculations of asymptotic averages and correlation integrals. We discuss how our approach generalizes the Schnakenberg decomposition of the average entropy-production rate, and how it unifies previous work. The application of our results to concrete models is presented in an accompanying publication. [less ▲]

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See detailLocal search methods based on variable focusing for random K-satisfiability
Lemoy, Rémi UL; Alava, Mikko; Aurell, Erik

in PHYSICAL REVIEW E (2015), 91(1), 013305-6

We introduce variable focused local search algorithms for satisfiabiliity problems. Usual approaches focus uniformly on unsatisfied clauses. The methods described here work by focusing on random variables ... [more ▼]

We introduce variable focused local search algorithms for satisfiabiliity problems. Usual approaches focus uniformly on unsatisfied clauses. The methods described here work by focusing on random variables in unsatisfied clauses. Variants are considered where variables are selected uniformly and randomly or by introducing a bias towards picking variables participating in several unsatistified clauses. These are studied in the case of the random 3-SAT problem, together with an alternative energy definition, the number of variables in unsatisfied constraints. The variable-based focused Metropolis search (V-FMS) is found to be quite close in performance to the standard clause-based FMS at optimal noise. At infinite noise, instead, the threshold for the linearity of solution times with instance size is improved by picking preferably variables in several UNSAT clauses. Consequences for algorithmic design are discussed. [less ▲]

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See detailStochastically driven single-level quantum dot: A nanoscale finite-time thermodynamic machine and its various operational modes
Esposito, Massimiliano UL; Kumar, Niraj; Lindenberg, Katja et al

in Physical Review E (2012), 85(3),

We describe a single-level quantum dot in contact with two leads as a nanoscale finite-time thermodynamic machine. The dot is driven by an external stochastic force that switches its energy between two ... [more ▼]

We describe a single-level quantum dot in contact with two leads as a nanoscale finite-time thermodynamic machine. The dot is driven by an external stochastic force that switches its energy between two values. In the isothermal regime, it can operate as a rechargeable battery by generating an electric current against the applied bias in response to the stochastic driving and then redelivering work in the reverse cycle. This behavior is reminiscent of the Parrondo paradox. If there is a thermal gradient the device can function as a work-generating thermal engine or as a refrigerator that extracts heat from the cold reservoir via the work input of the stochastic driving. The efficiency of the machine at maximum power output is investigated for each mode of operation, and universal features are identified. [less ▲]

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See detailStochastic thermodynamics under coarse graining
Esposito, Massimiliano UL

in Physical Review E (2012), 85(4),

A general formulation of stochastic thermodynamics is presented for open systems exchanging energy and particles with multiple reservoirs. By introducing a partition in terms of “mesostates” (e.g., sets ... [more ▼]

A general formulation of stochastic thermodynamics is presented for open systems exchanging energy and particles with multiple reservoirs. By introducing a partition in terms of “mesostates” (e.g., sets of “microstates”), the consequence on the thermodynamic description of the system is studied in detail. When microstates within mesostates rapidly thermalize, the entire structure of the microscopic theory is recovered at the mesostate level. This is not the case when these microstates remain out of equilibrium, leading to additional contributions to the entropy balance. Some of our results are illustrated for a model of two coupled quantum dots. [less ▲]

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See detailThermodynamics of a stochastic twin elevator
Kumar, Niraj; Van den Broeck, Christian; Esposito, Massimiliano UL et al

in Physical Review E (2011), 84(5),

We study the nonequilibrium thermodynamics of a single particle with two available energy levels, in contact with a classical (Maxwell-Boltzmann) or quantum (Bose-Einstein) heat bath. The particle can ... [more ▼]

We study the nonequilibrium thermodynamics of a single particle with two available energy levels, in contact with a classical (Maxwell-Boltzmann) or quantum (Bose-Einstein) heat bath. The particle can undergo transitions between the levels via thermal activation or deactivation. The energy levels are alternately raised at a given rate regardless of occupation by the particle, maintaining a fixed energy gap equal to ε between them. We explicitly calculate the work, heat, and entropy production rates. The efficiency in both the classical and the quantum case goes to a limit between 100 and 50% that depends on the relative rates of particle transitions and level elevation. In the classical problem we explicitly find the large deviation functions for heat, work, and internal energy. [less ▲]

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See detailThree faces of the second law. II. Fokker-Planck formulation
Van den Broeck, Christian; Esposito, Massimiliano UL

in Physical Review E (2010), 82(1),

The total entropy production is the sum of two contributions, the so-called adiabatic and nonadiabatic entropy productions, each of which is non-negative. We derive their explicit expressions for ... [more ▼]

The total entropy production is the sum of two contributions, the so-called adiabatic and nonadiabatic entropy productions, each of which is non-negative. We derive their explicit expressions for continuous Markovian processes, discuss their properties, and illustrate their behavior on two exactly solvable models. [less ▲]

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See detailThree faces of the second law. I. Master equation formulation
Esposito, Massimiliano UL; Van den Broeck, Christian

in Physical Review E (2010), 82(1),

We propose a formulation of stochastic thermodynamics for systems subjected to nonequilibrium constraints i.e. broken detailed balance at steady state and furthermore driven by external time-dependent ... [more ▼]

We propose a formulation of stochastic thermodynamics for systems subjected to nonequilibrium constraints i.e. broken detailed balance at steady state and furthermore driven by external time-dependent forces. A splitting of the second law occurs in this description leading to three second-law-like relations. The general results are illustrated on specific solvable models. The present paper uses a master equation based approach. [less ▲]

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See detailQuantum-dot Carnot engine at maximum power
Esposito, Massimiliano UL; Kawai, Ryoichi; Lindenberg, Katja et al

in Physical Review E (2010), 81(4),

We evaluate the efficiency at maximum power of a quantum-dot Carnot heat engine. The universal values of the coefficients at the linear and quadratic order in the temperature gradient are reproduced ... [more ▼]

We evaluate the efficiency at maximum power of a quantum-dot Carnot heat engine. The universal values of the coefficients at the linear and quadratic order in the temperature gradient are reproduced. Curzon-Ahlborn efficiency is recovered in the limit of weak dissipation. [less ▲]

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See detailPulse propagation in decorated granular chains: An analytical approach
Harbola, Upendra; Rosas, Alexandre; Romero, Aldo H. et al

in Physical Review E (2009), 80(5),

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See detailPulse propagation in tapered granular chains: An analytic study
Harbola, Upendra; Rosas, Alexandre; Esposito, Massimiliano UL et al

in Physical Review E (2009), 80(3),

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See detailPseudopath semiclassical approximation to transport through open quantum billiards: Dyson equation for diffractive scattering
Stampfer, C.; Rotter, S.; Burgdorfer, J. et al

in PHYSICAL REVIEW E (2005), 72(3),

We present a semiclassical theory for transport through open billiards of arbitrary convex shape that includes diffractively scattered paths at the lead openings. Starting from a Dyson equation for the ... [more ▼]

We present a semiclassical theory for transport through open billiards of arbitrary convex shape that includes diffractively scattered paths at the lead openings. Starting from a Dyson equation for the semiclassical Green's function we develop a diagrammatic expansion that allows a systematic summation over classical and pseudopaths, the latter consisting of classical paths joined by diffractive scatterings ("kinks"). This renders the inclusion of an exponentially proliferating number of pseudopath combinations numerically tractable for both regular and chaotic billiards. For a circular billiard and the Bunimovich stadium the path sum leads to a good agreement with the quantum path length power spectrum up to long path length. Furthermore, we find excellent numerical agreement with experimental studies of quantum scattering in microwave billiards where pseudopaths provide a significant contribution. [less ▲]

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See detailSemiclassical theory for transmission through open billiards: Convergence towards quantum transport
Wirtz, Ludger UL; Stampfer, C.; Rotter, S. et al

in PHYSICAL REVIEW E (2003), 67(1),

We present a semiclassical theory for transmission through open quantum billiards which converges towards quantum transport. The transmission amplitude can be expressed as a sum over all classical paths ... [more ▼]

We present a semiclassical theory for transmission through open quantum billiards which converges towards quantum transport. The transmission amplitude can be expressed as a sum over all classical paths and pseudopaths which consist of classical path segments joined by "kinks," i.e., diffractive scattering at lead mouths. For a rectangular billiard we show numerically that the sum over all such paths with a given number of kinks K converges to the quantum transmission amplitude as K-->infinity. Unitarity of the semiclassical theory is restored as K approaches infinity. Moreover, we find excellent agreement with the quantum path-length power spectrum up to very long path length. [less ▲]

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