Publications (24)46.24 Total impact
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ABSTRACT: We generalize stochastic thermodynamics to include information reservoirs. Such information reservoirs, which can be modeled as a sequence of bits, modify the second law. For example, work extraction from a system in contact with a single heat bath becomes possible if the system also interacts with an information reservoir. We obtain an inequality, and the corresponding fluctuation theorem, generalizing the standard entropy production of stochastic thermodynamics. From this inequality we can derive an information processing entropy production, which gives the second law in the presence of information reservoirs. We also develop a systematic linear response theory for information processing machines. For an unicyclic machine powered by an information reservoir, the efficiency at maximum power can deviate from the standard value 1/2. For the case where energy is consumed to erase the tape, the efficiency at maximum erasure is found to be 1/2.08/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We analyze a periodic optimal finitetime twostate informationdriven machine that extracts work from a single heat bath exploring imperfect measurements. Two models are considered, a memoryless one that ignores past measurements and an optimized model for which the feedback scheme consists of a protocol depending on the whole history of measurements. Depending on the precision of the measurement and on the period length the optimized model displays a phase transition to a phase where measurements are judged as nonreliable. We obtain the critical line exactly and show that the optimized model leads to more work extraction in comparison to the memoryless model, with the gain parameter being larger in the region where the frequency of nonreliable measurements is higher. We also demonstrate that the model has two second law inequalities, with the extracted work being bounded by the change of the entropy of the system and by the mutual information.06/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We show that a rate of conditional Shannon entropy reduction, characterizing the learning of an internal process about an external process, is bounded by the thermodynamic entropy production. This approach allows for the definition of an informational efficiency that can be used to study cellular information processing. We analyze three models of increasing complexity inspired by the E. coli sensory network, where the external process is an external ligand concentration jumping between two values. We start with a simple model for which ATP must be consumed so that a protein inside the cell can learn about the external concentration. With a second model for a single receptor we show that the rate at which the receptor learns about the external environment can be nonzero even without any dissipation inside the cell since chemical work done by the external process compensates for this learning rate. The third model is more complete, also containing adaptation. For this model we show inter alia that a bacterium in an environment that changes at a very slow timescale is quite inefficient, dissipating much more than it learns. Using the concept of a coarsegrained learning rate, we show for the model with adaptation that while the activity learns about the external signal the option of changing the methylation level increases the concentration range for which the learning rate is substantial.05/2014;  [Show abstract] [Hide abstract]
ABSTRACT: So far, feedbackdriven systems have been discussed using (i) measurement and control, (ii) a tape interacting with a system, or (iii) by identifying an implicit Maxwell demon in steadystate transport. We derive the corresponding second laws from one master fluctuation theorem and discuss their relationship. In particular, we show that both the entropy production involving mutual information between system and controller and the one involving a Shannon entropy difference of an information reservoir like a tape carry an extra term different from the usual current times affinity. We, thus, generalize stochastic thermodynamics to the presence of an information reservoir.Physical Review Letters 03/2014; 112(9):090601. · 7.73 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider the stationary state of a Markov process on a bipartite system from the perspective of stochastic thermodynamics. One subsystem is used to extract work from a heat bath while being affected by the second subsystem. We show that the latter allows for a transparent and thermodynamically consistent interpretation of a Maxwell's demon. Moreover, we obtain an integral fluctuation theorem involving the transfer entropy from one subsystem to the other. Comparing three different inequalities, we show that the entropy decrease of the first subsystem provides a tighter bound on the rate of extracted work than both the rate of transfer entropy from this subsystem to the demon and the heat dissipated through the dynamics of the demon. The latter two rates cannot be ordered by an inequality as shown with the illustrative example of a four state system.02/2014;  [Show abstract] [Hide abstract]
ABSTRACT: The problem of calculating the rate of mutual information between two coarsegrained variables that together specify a continuous time Markov process is addressed. As a main obstacle, the coarsegrained variables are in general nonMarkovian, therefore, an expression for their Shannon entropy rates in terms of the stationary probability distribution is not known. A numerical method to estimate the Shannon entropy rate of continuous time hiddenMarkov processes from a single time series is developed. With this method the rate of mutual information can be determined numerically. Moreover, an analytical upper bound on the rate of mutual information is calculated for a class of Markov processes for which the transition rates have a bipartite character. Our general results are illustrated with explicit calculations for fourstate networks.Journal of Statistical Physics 06/2013; 153(3). · 1.40 Impact Factor 
Article: Informationtheoretic versus thermodynamic entropy production in autonomous sensory networks.
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ABSTRACT: For sensory networks, we determine the rate with which they acquire information about the changing external conditions. Comparing this rate with the thermodynamic entropy production that quantifies the cost of maintaining the network, we find that there is no universal bound restricting the rate of obtaining information to be less than this thermodynamic cost. These results are obtained within a general bipartite model consisting of a stochastically changing environment that affects the instantaneous transition rates within the system. Moreover, they are illustrated with a simple fourstates model motivated by cellular sensing. On the technical level, we obtain an upper bound on the rate of mutual information analytically and calculate this rate with a numerical method that estimates the entropy of a time series generated with a simulation.Physical Review E 04/2013; 87(41):042104. · 2.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We present a finitetime detailed fluctuation theorem of the form P[over ̃](ΔS_{env})=e^{ΔS_{env}}P[over ̃](ΔS_{env}) for an appropriately weighted probability density P[over ̃](ΔS_{env}) of the external entropy production in the environment ΔS_{env}. The fluctuation theorem is valid for nonequilibrium systems with constant rates starting with an arbitrary initial probability distribution. We discuss the implication of this relation for the case of a temperature quench in classical equilibrium systems. The fluctuation theorem is tested numerically for a Markov jump process with six states and for a surface growth model.Physical Review E 04/2013; 87(41):042108. · 2.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Building on a model introduced by Mandal and Jarzynski [Proc. Natl. Acad. Sci. U. S. A., {\bf 109}, (2012) 11641], we present a simple version of an autonomous reversible Maxwell's demon. By changing the entropy of a tape consisting of a sequence of bits passing through the demon, the demon can lift a mass using the coupling to a heat bath. Our model becomes reversible by allowing the tape to move in both directions. In this thermodynamically consistent model, total entropy production consists of three terms one of which recovers the irreversible limit studied by MJ. Our demon allows an interpretation in terms of an enzyme transporting and transforming molecules between compartments. Moreover, both genuine equilibrium and a linear response regime with corresponding Onsager coefficients are well defined. Efficiency and efficiency at maximum power are calculated. In linear response, the latter is shown to be bounded by 1/2 if the demon operates as a machine and by 1/3 if it is operated as an eraser.EPL (Europhysics Letters) 02/2013; 101(6). · 2.26 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study the symmetry of large deviation functions associated with timeintegrated currents in Markov pure jump processes. One current known to have this symmetry is the fluctuating entropy production and this is the content of the fluctuation theorem. Here we obtain a necessary condition in order to have a current different from entropy with a symmetric large deviation function. This condition is related to degeneracies in the set of increments associated with fundamental cycles from Schnakenberg network theory. Moreover we consider 4states systems where we explicitly show that nonentropic timeintegrated currents can be symmetric. We also show that these new symmetries, as is the case of the fluctuation theorem, are related to timereversal. However, this becomes apparent only when stochastic trajectories are appropriately grouped together.Journal of Physics A Mathematical and Theoretical 07/2012; 45(48). · 1.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study the entropy production of a microscopic model for nonequilibrium wetting. We show that, in contrast to the equilibrium case, a bound interface in a nonequilibrium steady state produces entropy. Interestingly, in some regions of the phase diagram a bound interface produces more entropy than a free interface. Moreover, by solving exactly a foursite system, we find that the first derivative of the entropy production with respect to the control parameter displays a discontinuity at the critical point of the wetting transition.Journal of Physics A Mathematical and Theoretical 02/2012; 45(11):115005. · 1.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We investigate a new symmetry of the large deviation function of certain timeintegrated currents in nonequilibrium systems. The symmetry is similar to the wellknown GallavottiCohenEvansMorrisssymmetry for the entropy production, but it concerns a different functional of the stochatic trajectory. The symmetry can be found in a restricted class of Markov jump processes, where the network of microscopic transitions has a particular structure and the transition rates satisfy certain constraints. We provide three physical examples, where timeintegrated observables display such a symmetry. Moreover, we argue that the origin of the symmetry can be traced back to timereversal if stochastic trajectories are grouped appropriately.Journal of Statistical Physics 09/2011; · 1.40 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Models with a nonequilibrium wetting transition display a transition also in finite systems. This is different from nonequilibrium phase transitions into an absorbing state, where the stationary state is the absorbing one for any value of the control parameter in a finite system. In this paper, we study what kind of transition takes place in finite systems of nonequilibrium wetting models. By solving exactly a microscopic model with three and four sites and performing numerical simulations we show that the phase transition taking place in a finite system is characterized by the average interface height performing a random walk at criticality and does not discriminate between the boundedKPZ classes and the boundedEW class. We also study the finite size scaling of the bKPZ universality classes, showing that it presents peculiar features in comparison with other universality classes of nonequilibrium phase transitions.Journal of Statistical Mechanics Theory and Experiment 02/2011; 2011(02):P02036. · 1.87 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In a recent study (Miller and Shnerb 2010 arXiv:1011.3254) the contact process with a modified creation rate at a single site was shown to exhibit a nonuniversal scaling behavior with exponents varying with the creation rate at the special site. In the present work we argue that the survival probability decays according to a stretched exponential rather than a power law, explaining previous observations.Journal of Statistical Mechanics Theory and Experiment 02/2011; 2011(02):P02035. · 1.87 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study entropy production and fluctuation relations in the restricted solidonsolid growth model, which is a microscopic realization of the KPZ equation. Solving the one dimensional model exactly on a particular line of the phase diagram we demonstrate that entropy production quantifies the distance from equilibrium. Moreover, as an example of a physically relevant current different from the entropy, we study the symmetry of the large deviation function associated with the interface height. In a special case of a system of length L=4 we find that the probability distribution of the variation of height has a symmetric large deviation function, displaying a symmetry different from the GallavottiCohen symmetry. Comment: 21 pages, 5 figuresJournal of Statistical Mechanics Theory and Experiment 08/2010; · 1.87 Impact Factor 
Article: Nonequilibrium Wetting
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ABSTRACT: When a nonequilibrium growing interface in the presence of a wall is considered a nonequilibrium wetting transition may take place. This transition can be studied through Langevin equations or discrete growth models. In the first case, the KardarParisiZhang equation, which defines a very robust universality class for nonequilibrium moving interfaces, with a softwall potential is considered. While in the second, microscopic models, in the corresponding universality class, with evaporation and deposition of particles in the presence of hardwall are studied. Equilibrium wetting is related to a particular case of the problem, it corresponds to the EdwardsWilkinson equation with a potential in the continuum approach or to the fulfillment of detailed balance in the microscopic models. In this review we present the analytical and numerical methods used to investigate the problem and the very rich behavior that is observed with them. Wetting transitionsSurface growth modelsKardarParisiZhang equationJournal of Statistical Physics 01/2010; 138(4):728766. · 1.40 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study in further detail particle models displaying a boundaryinduced absorbing state phase transition [Deloubrière and van Wijland Phys. Rev. E 65, 046104 (2002) and Barato and Hinrichsen, Phys. Rev. Lett. 100, 165701 (2008)]. These are onedimensional systems consisting of a single site (the boundary) where creation and annihilation of particles occur, and a bulk where particles move diffusively. We study different versions of these models and confirm that, except for one exactly solvable bosonic variant exhibiting a discontinuous transition and trivial exponents, all the others display nontrivial behavior, with critical exponents differing from their meanfield values, representing a universality class. Finally, the relation of these systems with a (0+1)dimensional nonMarkovian process is discussed.Physical Review E 05/2009; 79(4 Pt 1):041130. · 2.31 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider a nonequilibrium process on a timeline with discrete sites which evolves following a nonMarkovian update rule in such a way that an active site at time t activates one or several sites in the future at time t+Δt. The time intervals Δt are distributed algebraically as (Δt)−1−κ, where 0<κ<1 is a control parameter. Depending on the activation rate, the system displays a nonequilibrium phase transition which may be interpreted as directed percolation transition driven by temporal Lévy flights in the limit of zero space dimensions. The critical properties are investigated by means of extensive numerical simulations and compared with fieldtheoretic predictions.Journal of Statistical Mechanics Theory and Experiment 01/2009; 2009:P02020. · 1.87 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We demonstrate that absorbing phase transitions in one dimension may be induced by the dynamics of a single site. As an example, we consider a onedimensional model of diffusing particles, where a single site at the boundary evolves according to the dynamics of a contact process. As the rate for offspring production at this site is varied, the model exhibits a phase transition from a fluctuating active phase into an absorbing state. The universal properties of the transition are analyzed by numerical simulations and approximation techniques.Physical Review Letters 04/2008; 100(16):165701. · 7.73 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study models for surface growth with a wetting and a roughening transition using simple and pair meanfield approximations. The simple meanfield equations are solved exactly and they predict the roughening transition and the correct growth exponents in a region of the phase diagram. The pair meanfield equations, which are solved numerically, show a better accordance with numerical simulation and correctly predicts a growing interface with constant velocity at the moving phase. Also, when detailed balance is fulfilled, the pair mean field becomes the exact solution of the model.Journal of Physics A Mathematical and Theoretical 04/2008; · 1.77 Impact Factor
Publication Stats
60  Citations  
46.24  Total Impact Points  
Top Journals
Institutions

2012–2014

Universität Stuttgart
Stuttgart, BadenWürttemberg, Germany


2011–2012

Abdus Salam International Centre for Theoretical Physics
Trst, Friuli Venezia Giulia, Italy


2008–2010

University of Wuerzburg
 Faculty of Physics and Astronomy
Würzburg, Bavaria, Germany
