Showing papers by "Udo Seifert published in 2017"
TL;DR: It is shown that this relation holds not only for the long-time limit of fluctuations, as described by large deviation theory, but also for fluctuations on arbitrary finite time scales, which facilitates applying the thermodynamic uncertainty relation to single molecule experiments, for which infinite time scales are not accessible.
Abstract: For fluctuating currents in nonequilibrium steady states, the recently discovered thermodynamic uncertainty relation expresses a fundamental relation between their variance and the overall entropic cost associated with the driving. We show that this relation holds not only for the long-time limit of fluctuations, as described by large deviation theory, but also for fluctuations on arbitrary finite time scales. This generalization facilitates applying the thermodynamic uncertainty relation to single molecule experiments, for which infinite time scales are not accessible. Importantly, often this finite-time variant of the relation allows inferring a bound on the entropy production that is even stronger than the one obtained from the long-time limit. We illustrate the relation for the fluctuating work that is performed by a stochastically switching laser tweezer on a trapped colloidal particle.
174 citations
TL;DR: General upper bounds on both the coherent and the total power of cyclic heat engines are derived, implying that, for sufficiently slow driving, coherence inevitably leads to power losses in the linear-response regime.
Abstract: We identify a universal indicator for the impact of coherence on periodically driven quantum devices by dividing their power output into a classical contribution and one stemming solely from superpositions. Specializing to Lindblad dynamics and small driving amplitudes, we derive general upper bounds on both the coherent and the total power of cyclic heat engines. These constraints imply that, for sufficiently slow driving, coherence inevitably leads to power losses in the linear-response regime. We illustrate our theory by working out the experimentally relevant example of a single-qubit engine.
124 citations
TL;DR: Universal bounds on this rate function follow which prove and generalize the thermodynamic uncertainty relation that quantifies the inevitable trade-off between cost and precision of any biomolecular process.
Abstract: In these lecture notes, the basic principles of stochastic thermodynamics are developed starting with a closed system in contact with a heat bath. A trajectory undergoes Markovian transitions between observable meso-states that correspond to a coarse-grained description of, e.g., a biomolecule or a biochemical network. By separating the closed system into a core system and into reservoirs for ligands and reactants that bind to, and react with the core system, a description as an open system controlled by chemical potentials and possibly an external force is achieved. Entropy production and further thermodynamic quantities defined along a trajectory obey various fluctuation theorems. For describing fluctuations in a non-equilibrium steady state in the long-time limit, the concept of a rate function for large deviations from the mean behavior is derived from the weight of a trajectory. Universal bounds on this rate function follow which prove and generalize the thermodynamic uncertainty relation that quantifies the inevitable trade-off between cost and precision of any biomolecular process. Specific illustrations are given for molecular motors, Brownian clocks and enzymatic networks that show how these tools can be used for thermodynamic inference of hidden properties of a system.
87 citations
TL;DR: The proteins that adhere cells together in tissue assemble in domains near the cell–cell interface that are regulated by the membrane itself — with an explicit role for fluctuations.
Abstract: The integrity of living tissues is maintained by adhesion domains of trans-bonds formed between cadherin proteins residing on opposing membranes of neighbouring cells. These domains are stabilized by lateral cis-interactions between the cadherins on the same cell. However, the origin of cis-interactions remains perplexing since they are detected only in the context of trans-bonds. By combining experimental, analytical and computational approaches, we identify bending fluctuations of membranes as a source of long-range cis-interactions, and a regulator of trans-interactions. Specifically, nanometric membrane bending and fluctuations introduce cooperative effects that modulate the affinity and binding/unbinding rates for trans-dimerization, dramatically affecting the nucleation and growth of adhesion domains. Importantly, this regulation relies on physical principles and not on details of protein–protein interactions. These omnipresent fluctuations can thus act as a generic control mechanism in all types of cell adhesion, suggesting a hitherto unknown physiological role for recently identified active fluctuations of cellular membranes. The proteins that adhere cells together in tissue assemble in domains near the cell–cell interface. Experiments, simulations and theory show that formation of these domains is regulated by the membrane itself — with an explicit role for fluctuations.
82 citations
TL;DR: Stochastic thermodynamics is used to analyze the learning of a classification rule by a neural network and it is shown that the information acquired by the network is bounded by the thermodynamic cost of learning and a learning efficiency is introduced.
Abstract: Virtually every organism gathers information about its noisy environment and builds models from those data, mostly using neural networks. Here, we use stochastic thermodynamics to analyze the learning of a classification rule by a neural network. We show that the information acquired by the network is bounded by the thermodynamic cost of learning and introduce a learning efficiency $\ensuremath{\eta}\ensuremath{\le}1$. We discuss the conditions for optimal learning and analyze Hebbian learning in the thermodynamic limit.
48 citations
TL;DR: It is shown that the number of coherent oscillations that quantifies the precision of the oscillator is universally bounded by the thermodynamic force that drives the system out of equilibrium and by the topology of the underlying biochemical network of states.
Abstract: Biochemical oscillations are prevalent in living organisms. Systems with a small number of constituents cannot sustain coherent oscillations for an indefinite time because of fluctuations in the period of oscillation. We show that the number of coherent oscillations that quantifies the precision of the oscillator is universally bounded by the thermodynamic force that drives the system out of equilibrium and by the topology of the underlying biochemical network of states. Our results are valid for arbitrary Markov processes, which are commonly used to model biochemical reactions. We apply our results to a model for a single KaiC protein and to an activator-inhibitor model that consists of several molecules. From a mathematical perspective, based on strong numerical evidence, we conjecture a universal constraint relating the imaginary and real parts of the first nontrivial eigenvalue of a stochastic matrix.
46 citations
TL;DR: In this paper, a thermodynamically consistent minimal lattice model that includes the chemical reaction providing the propulsion and ordinary translational noise was proposed to identify the physical entropy production of an active particle in an external potential.
Abstract: Entropy production of an active particle in an external potential is identified through a thermodynamically consistent minimal lattice model that includes the chemical reaction providing the propulsion and ordinary translational noise. In the continuum limit, a unique expression follows, comprising a direct contribution from the active process and an indirect contribution from ordinary diffusive motion. From the corresponding Langevin equation, this physical entropy production cannot be inferred through the conventional, yet here ambiguous, comparison of forward and time-reversed trajectories. Generalizations to several interacting active particles and passive particles in a bath of active ones are presented explicitly, further ones are briefly indicated.
40 citations
TL;DR: In this article, the authors derive a refined second law for small molecular machines that include this cost, which is, for example, generated by free energy consumption of a chemical reaction that modifies the energy landscape for such a machine.
Abstract: Artificial molecular machines are often driven by the periodic variation of an external parameter. This external control exerts work on the system of which a part can be extracted as output if the system runs against an applied load. Usually, the thermodynamic cost of the process that generates the external control is ignored. Here, we derive a refined second law for such small machines that include this cost, which is, for example, generated by free energy consumption of a chemical reaction that modifies the energy landscape for such a machine. In the limit of irreversible control, this refined second law becomes the standard one. Beyond this ideal limiting case, our analysis shows that due to a new entropic term unexpected regimes can occur: the control work can be smaller than the extracted work and the work required to generate the control can be smaller than this control work. Our general inequalities are illustrated by a paradigmatic three-state system.
32 citations
TL;DR: A refined second law is derived for small machines that include the thermodynamic cost of the process that generates the external control and shows that due to a new entropic term unexpected regimes can occur: the control work can be bigger than the extracted work and the work required to generate the control can be smaller than this control work.
Abstract: Artificial molecular machines are often driven by the periodic variation of an external parameter. This external control exerts work on the system of which a part can be extracted as output if the system runs against an applied load. Usually, the thermodynamic cost of the process that generates the external control is ignored. Here, we derive a refined second law for such small machines that include this cost, which is, for example, generated by free energy consumption of a chemical reaction that modifies the energy landscape for such a machine. In the limit of irreversible control, this refined second law becomes the standard one. Beyond this ideal limiting case, our analysis shows that due to a new entropic term unexpected regimes can occur: The control work can be smaller than the extracted work and the work required to generate the control can be smaller than this control work. Our general inequalities are illustrated by a paradigmatic three-state system.
19 citations
TL;DR: The thermodynamic bounds for ultra-affinity are established, and it is shown that the same reaction scheme can in principle be used both to strengthen and to weaken affinities (leading in this case to infra-Affinity), and that cofactors are essential to achieve affinity beyond the equilibrium range.
19 citations
TL;DR: In this article, the authors apply the concept of frequency-dependent effective temperature based on the fluctuation-dissipation ratio to a driven Brownian particle in a nonequilibrium steady state.
Abstract: We apply the concept of a frequency-dependent effective temperature based on the fluctuation-dissipation ratio to a driven Brownian particle in a nonequilibrium steady state. Using this system as a thermostat for a weakly coupled harmonic oscillator, the oscillator thermalizes according to a canonical distribution at the respective effective temperature across the entire frequency spectrum. By turning the oscillator from a passive thermometer into a heat engine, we realize the cyclic extraction of work from a single thermal reservoir, which is feasible only due to its nonequilibrium nature.
TL;DR: Using stochastic thermodynamics, it is shown that the thermodynamic costs of the learning process provide an upper bound on the amount of information that the network is able to learn from its teacher for both batch and online learning.
Abstract: Biological systems have to build models from their sensory data that allow them to efficiently process previously unseen inputs. Here, we study a neural network learning a linearly separable rule using examples provided by a teacher. We analyse the ability of the network to apply the rule to new inputs, that is to generalise from past experience. Using stochastic thermodynamics, we show that the thermodynamic costs of the learning process provide an upper bound on the amount of information that the network is able to learn from its teacher for both batch and online learning. This allows us to introduce a thermodynamic efficiency of learning. We analytically compute the dynamics and the efficiency of a noisy neural network performing online learning in the thermodynamic limit. In particular, we analyse three popular learning algorithms, namely Hebbian, Perceptron and AdaTron learning. Our work extends the methods of stochastic thermodynamics to a new type of learning problem and might form a suitable basis for investigating the thermodynamics of decision-making.
TL;DR: The nonequilibrium forces mediated by the depletants on the two colloidal particles within a dynamical superposition approximation (DSA) scheme are calculated and the colloidal microstructure around the driven probe is obtained.
Abstract: Entropic depletion forces arise between mesoscopic bodies that are immersed in a suspension of macromolecules, such as colloid-polymer mixtures. Here we consider the case of a driven colloidal probe in the presence of another, passive colloidal particle, both solvated in an ideal bath of small spherical particles. We calculate the nonequilibrium forces mediated by the depletants on the two colloidal particles within a dynamical superposition approximation (DSA) scheme. In order to assess the quality of this approximation, and to obtain the colloidal microstructure around the driven probe, we corroborate our theoretical results with Brownian dynamics simulations.
TL;DR: In this article, a neural network learns a binary classification rule for new inputs from examples provided by a teacher, and analytically computes the dynamics and the efficiency of a noisy neural network performing online learning in the thermodynamic limit.
Abstract: Biological systems have to build models from their sensory input data that allow them to efficiently process previously unseen inputs. Here, we study a neural network learning a binary classification rule for these inputs from examples provided by a teacher. We analyse the ability of the network to apply the rule to new inputs, that is to generalise from past experience. Using stochastic thermodynamics, we show that the thermodynamic costs of the learning process provide an upper bound on the amount of information that the network is able to learn from its teacher for both batch and online learning. This allows us to introduce a thermodynamic efficiency of learning. We analytically compute the dynamics and the efficiency of a noisy neural network performing online learning in the thermodynamic limit. In particular, we analyse three popular learning algorithms, namely Hebbian, Perceptron and AdaTron learning. Our work extends the methods of stochastic thermodynamics to a new type of learning problem and might form a suitable basis for investigating the thermodynamics of decision-making.
TL;DR: In this paper, a modified fluctuation theorem for entropy production is shown to hold in the large deviation limit for discrete bipartite systems with slow degrees of freedom, where it is not possible to infer the amount of produced entropy exactly.
Abstract: The fluctuation theorem for entropy production is a remarkable symmetry of the distribution of produced entropy that holds universally in non-equilibrium steady states with Markovian dynamics. However, in systems with slow degrees of freedom that are hidden from the observer, it is not possible to infer the amount of produced entropy exactly. Previous work suggested that a relation similar to the fluctuation theorem may hold at least approximately for such systems if one considers an apparent entropy production. By extending the notion of apparent entropy production to discrete bipartite systems, we investigate which criteria have to be met for such a modified fluctuation theorem to hold in the large deviation limit. We use asymptotic approximations of the large deviation function to show that the probabilities of extreme events of apparent entropy production always obey a modified fluctuation theorem and, moreover, that it is possible to infer otherwise hidden properties. For the paradigmatic case of two coupled colloidal particles on rings the rate function of the apparent entropy production is calculated to illustrate this asymptotic behavior and to show that the modified fluctuation theorem observed experimentally for short observation times does not persist in the long time limit.
TL;DR: In this article, extensive simulations are performed, studying the fractal dimension and the dynamics of growth of a patch on a particle of a finite size, as a function of the initial density and the binding affinity of diffusing tracers.
Abstract: Dendrite growth of metal patches on colloidal particles shows a variety of structures depending on the preparation conditions. The morphology of these patches suggests a cross-over from a reaction to a diffusion limited growth, implicating diffusion on the particle surface. Interestingly, the morphological and optical characteristics of the patches continuously change between two limiting behaviors. To understand this growth process, extensive simulations are performed, studying the fractal dimension and the dynamics of growth of a patch on a particle of a finite size, as a function of the initial density and the binding affinity of diffusing tracers. Several important growth regimes are characterized that enable to optimize the pathway for the synthesis of optically active, patchy particles.