arXiv subjects

Udo Seifert

Publications and source records attributed to Udo Seifert.

At least 73 records · Page 4Linked to original sources

arXiv2017

Stochastic thermodynamics: From principles to the cost of precision

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 behaviour 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.

cond-mat.stat-mech↗

arXiv2017

Finite-time generalization of the thermodynamic uncertainty relation

For fluctuating currents in non-equilibrium 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 timescales 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.

cond-mat.stat-mech↗

arXiv2017

Thermodynamic efficiency of learning a rule in neural networks

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.

cond-mat.stat-mech↗

arXiv2017

Coherence of Biochemical Oscillations is Bounded by Driving Force and Network Topology

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 non-trivial eigenvalue of a stochastic matrix.

cond-mat.stat-mech↗

arXiv2017

Thermodynamic bounds on the ultra- and infra-affinity of Hsp70 for its substrates

The 70 kDa Heat Shock Proteins Hsp70 have several essential functions in living systems, such as protecting cells against protein aggregation, assisting protein folding, remodeling protein complexes and driving the translocation into organelles. These functions require high affinity for non-specific amino-acid sequences that are ubiquitous in proteins. It has been recently shown that this high affinity, called ultra-affinity, depends on a process driven out of equilibrium by ATP hydrolysis. Here we establish the thermodynamic bounds for ultra-affinity, and further show that the same reaction scheme can in principle be used both to strengthen and to weaken affinities (leading in this case to infra-affinity). We show that cofactors are essential to achieve affinity beyond the equilibrium range. Finally, biological implications are discussed.

q-bio.BM↗

arXiv2017

Driven Brownian particle as a paradigm for a nonequilibrium heat bath: Effective temperature and cyclic work extraction

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.

cond-mat.stat-mech↗

arXiv2017

Universal Coherence-Induced Power Losses of Quantum Heat Engines in Linear Response

We introduce a universal scheme to divide the power output of a periodically driven quantum heat engine into a classical contribution and one stemming solely from quantum coherence. Specializing to Lindblad-dynamics and small driving amplitudes, we derive general upper bounds on both, the coherent and the total power. These constraints imply that, in the linear-response regime, coherence inevitably leads to power losses. To illustrate our general analysis, we explicitly work out the experimentally relevant example of a single-qubit engine.

cond-mat.stat-mech↗

arXiv2017

Cost and Precision of Brownian Clocks

Brownian clocks are biomolecular networks that can count time. A paradigmatic example are proteins that go through a cycle thus regulating some oscillatory behaviour in a living system. Typically, such a cycle requires free energy often provided by ATP hydrolysis. We investigate the relation between the precision of such a clock and its thermodynamic costs. For clocks driven by a constant thermodynamic force, a given precision requires a minimal cost that diverges as the uncertainty of the clock vanishes. In marked contrast, we show that a clock driven by a periodic variation of an external protocol can achieve arbitrary precision at arbitrarily low cost. This result constitutes a fundamental difference between processes driven by a fixed thermodynamic force and those driven periodically. As a main technical tool, we map a periodically driven system with a deterministic protocol to one subject to an external protocol that changes in stochastic time intervals, which simplifies calculations significantly. In the non-equilibrium steady state of the resulting bipartite Markov process, the uncertainty of the clock can be deduced from the calculable dispersion of a corresponding current.

cond-mat.stat-mech↗

arXiv2017

Universal bound on the efficiency of molecular motors

The thermodynamic uncertainty relation provides an inequality relating any mean current, the associated dispersion and the entropy production rate for arbitrary non-equilibrium steady states. Applying it here to a general model of a molecular motor running against an external force or torque, we show that the thermodynamic efficiency of such motors is universally bounded by an expression involving only experimentally accessible quantities. For motors pulling cargo through a viscous fluid, a universal bound for the corresponding Stokes efficiency follows as a variant. A similar result holds if mechanical force is used to synthesize molecules of high chemical potential. Crucially, no knowledge of the detailed underlying mechano-chemical mechanism is required for applying these bounds.

cond-mat.stat-mech↗

arXiv2016

Energetics of synchronization in coupled oscillators rotating on circular trajectories

We derive a concise and general expression of the energy dissipation rate for coupled oscillators rotating on circular trajectories by unifying the nonequilibrium aspects with the nonlinear dynamics via stochastic thermodynamics. In the framework of phase oscillator models, it is known that the even and odd parts of the coupling function express the effect on collective and relative dynamics, respectively. We reveal that the odd part always decreases the dissipation upon synchronization, while the even part yields a characteristic square-root change of the dissipation near the bifurcation point whose sign depends on the specific system parameters. We apply our theory to hydrodynamically coupled Stokes spheres rotating on circular trajectories that can be interpreted as a simple model of synchronization of coupled oscillators in a biophysical system. We show that the coupled Stokes spheres gain the ability to do more work on the surrounding fluid as the degree of phase synchronization increases.

nlin.AO↗

arXiv2016

Stochastic Thermodynamics of Learning

Virtually every organism gathers information about its noisy environment and builds models from that data, mostly using neural networks. Here, we use stochastic thermodynamics to analyse 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 $η\le1$. We discuss the conditions for optimal learning and analyse Hebbian learning in the thermodynamic limit.

cond-mat.stat-mech↗

arXiv2016

Optimal inference strategies and their implications for the linear noise approximation

We study the information loss of a class of inference strategies that is solely based on time averaging. For an array of independent binary sensors (e.g., receptors, single electron transistors) measuring a weak random signal (e.g., ligand concentration, gate voltage) this information loss is up to 0.5 bit per measurement irrespective of the number of sensors. We derive a condition related to the local detailed balance relation that determines whether or not such a loss of information occurs. Specifically, if the free energy difference arising from the signal is symmetrically distributed among the forward and backward rates, time integration mechanisms will capture the full information about the signal. As an implication, for the linear noise approximation, we can identify the same loss of information, arising from its inherent simplification of the dynamics.

cond-mat.stat-mech↗

arXiv2016

Affinity- and topology-dependent bound on current fluctuations

We provide a proof of a recently conjectured universal bound on current fluctuations in Markovian processes. This bound establishes a link between the fluctuations of an individual observable current, the cycle affinities driving the system into a non-equilibrium steady state, and the topology of the network. The proof is based on a decomposition of the network into independent cycles with both positive affinity and positive stationary cycle current. This formalism allows for a refinement of the bound for systems in equilibrium or with locally vanishing affinities.

cond-mat.stat-mech↗

arXiv2016

Universal bounds on current fluctuations

For current fluctuations in non-equilibrium steady states of Markovian processes, we derive four different universal bounds valid beyond the Gaussian regime. Different variants of these bounds apply to either the entropy change or any individual current, e.g., the rate of substrate consumption in a chemical reaction or the electron current in an electronic device. The bounds vary with respect to their degree of universality and tightness. A universal parabolic bound on the generating function of an arbitrary current depends solely on the average entropy production. A second, stronger bound requires knowledge both of the thermodynamic forces that drive the system and of the topology of the network of states. These two bounds are conjectures based on extensive numerics. An exponential bound that depends only on the average entropy production and the average number of transitions per time is rigorously proved. This bound has no obvious relation to the parabolic bound but it is typically tighter further away from equilibrium. An asymptotic bound that depends on the specific transition rates and becomes tight for large fluctuations is also derived. This bound allows for the prediction of the asymptotic growth of the generating function. Even though our results are restricted to networks with a finite number of states, we show that the parabolic bound is also valid for three paradigmatic examples of driven diffusive systems for which the generating function can be calculated using the additivity principle. Our bounds provide a new general class of constraints for nonequilibrium systems.

cond-mat.stat-mech↗

arXiv2016

Extreme fluctuations of active Brownian motion

In active Brownian motion, an internal propulsion mechanism interacts with translational and rotational thermal noise and other internal fluctuations to produce directed motion. We derive the distribution of its extreme fluctuations and identify its universal properties using large deviation theory. The limits of slow and fast internal dynamics give rise to a kink-like and parabolic behavior of the corresponding rate functions, respectively. For dipolar Janus particles in two and three dimensions interacting with a field, we predict a novel symmetry akin to, but different from, the one related to entropy production. Measurements of these extreme fluctuations could thus be used to infer properties of the underlying, often hidden, network of states.

cond-mat.stat-mech↗

arXiv2016

Periodic Thermodynamics of Open Quantum Systems

The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and second law are formulated consistently. In the linear response regime, entropy production becomes a quadratic form in the affinities. Specializing to Lindblad-dynamics, we identify the corresponding kinetic coefficients in terms of correlation functions of the unperturbed dynamics. Reciprocity relations follow from symmetries with respect to time reversal. The kinetic coefficients can be split into a classical and a quantum contribution subject to a new constraint, which follows from a natural detailed balance condition. This constraint implies universal bounds on efficiency and power of quantum heat engines. In particular, we show that Carnot efficiency can not be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian. For illustration, we specialize our universal results to a driven two-level system in contact with a heat bath of sinusoidally modulated temperature.

cond-mat.stat-mech↗

arXiv2016

Stochastic thermodynamics of resetting

Stochastic dynamics with random resetting leads to a non-equilibrium steady state. Here, we consider the thermodynamics of resetting by deriving the first and second law for reset processes far from equilibrium. We identify the contributions to the entropy production of the system which arise due to resetting and show that they correspond to the rate with which information is either erased or created. Using Landauer's principle, we derive a bound on the amount of work that is required to maintain a resetting process. We discuss different regimes of resetting, including a Maxwell's demon scenario where heat is extracted from a bath at constant temperature.

cond-mat.stat-mech↗

arXiv2016

Optimal performance of periodically driven, stochastic heat engines under limited control

We consider the performance of periodically driven stochastic heat engines in the linear response regime. Reaching the theoretical bounds for efficiency and efficiency at maximum power typically requires full control over the design and the driving of the system. We develop a framework which allows to quantify the role that limited control over the system has on the performance. Specifically, we show that optimizing the driving entering the work extraction for a given temperature protocol leads to a universal, one-parameter dependence for both maximum efficiency and maximum power as a function of efficiency. In particular, we show that reaching Carnot efficiency (and, hence, Curzon-Ahlborn efficiency at maximum power) requires to have control over the amplitude of the full Hamiltonian of the system. Since the kinetic energy cannot be controlled by an external parameter, heat engines based on underdamped dynamics can typically not reach Carnot efficiency. We illustrate our general theory with a paradigmatic case study of a heat engine consisting of an underdamped charged particle in a modulated two-dimensional harmonic trap in the presence of a magnetic field.

cond-mat.stat-mech↗