Showing papers by "Udo Seifert published in 2022"

Thermodynamic Inference in Partially Accessible Markov Networks: A Unifying Perspective from Transition-Based Waiting Time Distributions

Abstract: The inference of thermodynamic quantities from the description of an only partially accessible physical system is a central challenge in stochastic thermodynamics. A common approach is coarse-graining, which maps the dynamics of such a system to a reduced effective one. While coarse-graining states of the system into compound ones is a well-studied concept, recent evidence hints at a complementary description by considering observable transitions and waiting times. In this work, we consider waiting time distributions between two consecutive transitions of a partially observable Markov network. We formulate an entropy estimator using their ratios to quantify irreversibility. Depending on the complexity of the underlying network, we formulate criteria to infer whether the entropy estimator recovers the full physical entropy production or whether it just provides a lower bound that improves on established results. This conceptual approach, which is based on the irreversibility of underlying cycles, additionally enables us to derive estimators for the topology of the network, i.e., the presence of a hidden cycle, its number of states, and its driving affinity. Adopting an equivalent semi-Markov description, our results can be condensed into a fluctuation theorem for the corresponding semi-Markov process. This mathematical perspective provides a unifying framework for the entropy estimators considered here and established earlier ones. The crucial role of the correct version of time reversal helps to clarify a recent debate on the meaning of formal versus physical irreversibility. Extensive numerical calculations based on a direct evaluation of waiting time distributions illustrate our exact results and provide an estimate on the quality of the bounds for affinities of hidden cycles. DOI:

Anomalous relaxation from a non-equilibrium steady state: An isothermal analog of the Mpemba effect

Abstract: The Mpemba effect denotes an anomalous relaxation phenomenon where a system initially at a hot temperature cools faster than a system that starts at a less elevated temperature. We introduce an isothermal analog of this effect for a system prepared in a non-equilibrium steady state that then relaxes towards equilibrium. Here, the driving strength, which determines the initial non-equilibrium steady state, takes the role of the temperature in the original version. As a paradigm, we consider a particle initially driven by a non-conservative force along a one-dimensional periodic potential. We show that for an asymmetric potential relaxation from a strongly driven initial state is faster than from a more weakly driven one at least for one of the two possible directions of driving. These results are first obtained through perturbation theory in the strength of the potential and then extended to potentials of arbitrary strength through topological arguments.

The Two Scaling Regimes of the Thermodynamic Uncertainty Relation for the KPZ-Equation

Abstract: We investigate the thermodynamic uncertainty relation for the $$(1+1)$$ dimensional Kardar–Parisi–Zhang (KPZ) equation on a finite spatial interval. In particular, we extend the results for small coupling strengths obtained previously to large values of the coupling parameter. It will be shown that, due to the scaling behavior of the KPZ equation, the thermodynamic uncertainty relation (TUR) product displays two distinct regimes which are separated by a critical value of an effective coupling parameter. The asymptotic behavior below and above the critical threshold is explored analytically. For small coupling, we determine this product perturbatively including the fourth order; for strong coupling we employ a dynamical renormalization group approach. Whereas the TUR product approaches a value of 5 in the weak coupling limit, it asymptotically displays a linear increase with the coupling parameter for strong couplings. The analytical results are then compared to direct numerical simulations of the KPZ equation showing convincing agreement.

First-Principle Coarse-Graining Framework for Scale-Free Bell-Like Association and Dissociation Rates in Thermal and Active Systems

Abstract: A new theory of ligand-receptor bonds in biological cells that accounts for membrane fluctuations reveals an orders-of-magnitude increase in binding rates and the range over which a receptor can recognize its ligand.

Thermodynamic Uncertainty Relation in Interacting Many-Body Systems.

Abstract: The thermodynamic uncertainty relation (TUR) has been well studied for systems with few degrees of freedom. While, in principle, the TUR holds for more complex systems with many interacting degrees of freedom as well, little is known so far about its behavior in such systems. We analyze the TUR in the thermodynamic limit for mixtures of driven particles with short-range interactions. Our main result is an explicit expression for the optimal estimate of the total entropy production in terms of single-particle currents and correlations between two-particle currents. Quantitative results for various versions of a driven lattice gas demonstrate the practical implementation of this approach.

Time-Resolved Statistics of Snippets as General Framework for Model-Free Entropy Estimators.

Abstract: Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time reversal like a current. We introduce a general framework that allows us to infer a lower bound on entropy production through measuring the time-resolved statistics of events with any symmetry under time reversal, in particular, time-symmetric instantaneous events. We emphasize Markovianity as a property of certain events rather than of the full system and introduce an operationally accessible criterion for this weakened Markov property. Conceptually, the approach is based on snippets as particular sections of trajectories between two Markovian events, for which a generalized detailed balance relation is discussed.

Coherence of oscillations in the weak-noise limit.

Abstract: In a noisy environment, oscillations lose their coherence, which can be characterized by a quality factor. We determine this quality factor for oscillations arising from a driven Fokker-Planck dynamics along a periodic one-dimensional potential analytically in the weak-noise limit. With this expression, we can prove for this continuum model the analog of an upper bound that has been conjectured for the coherence of oscillations in discrete Markov network models. We show that our approach can also be adapted to motion along a noisy two-dimensional limit cycle. Specifically, we apply our scheme to the noisy Stuart-Landau oscillator and the thermodynamically consistent Brusselator as a simple model for a chemical clock. Our approach thus complements the fairly sophisticated extant general framework based on techniques from Hamilton-Jacobi theory with which we compare our results numerically.