arXiv subjects

Aljaž Godec

Publications and source records attributed to Aljaž Godec.

At least 37 records · Page 2Linked to original sources

arXiv2024

Thermodynamic bounds on generalized transport: From single-molecule to bulk observables

We prove that the transport of any differentiable scalar observable in $d$-dimensional non-equilibrium systems is bounded from above by the total entropy production scaled by the amount the observation "stretches" microscopic coordinates. The result--a time-integrated generalized speed limit--reflects the thermodynamic cost of transport of observables, and places underdamped and overdamped stochastic dynamics on equal footing with deterministic motion. Our work allows for stochastic thermodynamics to make contact with bulk experiments, and fills an important gap in thermodynamic inference, since microscopic dynamics is, at least for short times, underdamped. Requiring only averages but not sample-to-sample fluctuations, the proven transport bound is practical and applicable not only to single-molecule but also bulk experiments where only averages are observed, which we demonstrate by examples. Our results may facilitate thermodynamic inference on molecular machines without an obvious directionality from bulk observations of transients probed, e.g.\ in time-resolved X-ray scattering.

cond-mat.stat-mech↗

arXiv2024

Model-free inference of memory in conformational dynamics of a multi-domain protein

Single-molecule experiments provide insight into the motion (conformational dynamics) of individual protein molecules. Usually, a well-defined but coarse-grained intramolecular coordinate is measured and subsequently analysed with the help of Hidden Markov Models (HMMs) to deduce the kinetics of protein conformational changes. Such approaches rely on the assumption that the microscopic dynamics of the protein evolve according to a Markov-jump process on some network. However, the manifestation and extent of memory in the dynamics of the observable strongly depends on the chosen underlying Markov model, which is generally not known and therefore can lead to misinterpretations. Here, we combine extensive single-molecule plasmon ruler experiments on the heat shock protein Hsp90, computer simulations, and theory to infer and quantify memory in a model-free fashion. Our analysis is based on the bare definition of non-Markovian behaviour and does not require any underlying model. In the case of Hsp90 probed by a plasmon ruler, the Markov assumption is found to be clearly and conclusively violated on timescales up to roughly 50 s, which corresponds roughly to $\sim$50% of the inferred correlation time of the signal. The extent of memory is striking and reaches biologically relevant timescales. This implies that memory effects penetrate even the slowest observed motions. We provide clear and reproducible guidelines on how to test for the presence and duration of memory in experimental single-molecule data.

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arXiv2024

On the emergence of memory in equilibrium versus non-equilibrium systems

Experiments often probe observables that correspond to low-dimensional projections of highdimensional dynamics. In such situations distinct microscopic configurations become lumped into the same observable state. It is well known that correlations between the observable and the hidden degrees of freedom give rise to memory effects. However, how and under which conditions these correlations emerge remains poorly understood. Here we shed light on two fundamentally different scenarios of the emergence of memory in minimal stationary systems, where observed and hidden degrees of freedom evolve either cooperatively or are coupled by a hidden non-equilibrium current. In the reversible setting strongest memory manifests when the time-scales of hidden and observed dynamics overlap, whereas, strikingly, in the driven setting maximal memory emerges under a clear time-scale separation. Our results hint at the possibility of fundamental differences in the way memory emerges in equilibrium versus driven systems that may be utilized as a "diagnostic" of the underlying hidden transport mechanism.

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arXiv2023

Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime

We derive general bounds on the probability that the empirical first-passage time $\overlineτ_n\equiv \sum_{i=1}^nτ_i/n$ of a reversible ergodic Markov process inferred from a sample of $n$ independent realizations deviates from the true mean first-passage time by more than any given amount in either direction. We construct non-asymptotic confidence intervals that hold in the elusive small-sample regime and thus fill the gap between asymptotic methods and the Bayesian approach that is known to be sensitive to prior belief and tends to underestimate uncertainty in the small-sample setting. We prove sharp bounds on extreme first-passage times that control uncertainty even in cases where the mean alone does not sufficiently characterize the statistics. Our concentration-of-measure-based results allow for model-free error control and reliable error estimation in kinetic inference, and are thus important for the analysis of experimental and simulation data in the presence of limited sampling.

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arXiv2023

Milestoning estimators of dissipation in systems observed at a coarse resolution: When ignorance is truly bliss

Many non-equilibrium, active processes are observed at a coarse-grained level, where different microscopic configurations are projected onto the same observable state. Such "lumped" observables display memory, and in many cases the irreversible character of the underlying microscopic dynamics becomes blurred, e.g., when the projection hides dissipative cycles. As a result, the observations appear less irreversible, and it is very challenging to infer the degree of broken time-reversal symmetry. Here we show, contrary to intuition, that by ignoring parts of the already coarse-grained state space we may -- via a process called milestoning -- improve entropy-production estimates. Milestoning systematically renders observations "closer to underlying microscopic dynamics" and thereby improves thermodynamic inference from lumped data assuming a given range of memory. Moreover, whereas the correct general physical definition of time-reversal in the presence of memory remains unknown, we here show by means of systematic, physically relevant examples that at least for semi-Markov processes of first and second order, waiting-time contributions arising from adopting a naive Markovian definition of time-reversal generally must be discarded.

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arXiv2023

Vorticity and level-set variations of invariant current bound steady-state dissipation

A non-vanishing entropy production rate is a hallmark of non-equilibrium stationary states and is therefore at the heart of non-equilibrium thermodynamics. It is a manifestation of a steady circulation $J_{\rm inv}$ along the level sets of the invariant density $ρ_{\rm inv}$, and is thus generically used to quantify how far a steady system is driven out of equilibrium. While it is well known that there exists a continuum of distinct steady states with the same invariant measure, the question how the geometry and topology of the invariant current a priori affect dissipation remained elusive. For confined irreversible diffusions we identify two minimal descriptors, the $ρ_{\rm inv}$-weighted vorticity and the variation of $J_{\rm inv}$ along level sets of $ρ_{\rm inv}$, and prove that these jointly bound from above the steady-state entropy production rate. In regions where $ρ_{\rm inv}$ is close to Gaussian the bound is dominated solely by the vorticity of the drift field and in the low-noise (Freidlin-Wentzel) limit by any non-potential contribution to the drift, rendering $J_{\rm inv}$ virtually constant along the level sets of $ρ_{\rm inv}$.

math-ph↗

arXiv2023

Asymmetric Thermal Relaxation in Driven Systems: Rotations go Opposite Ways

It was predicted and recently experimentally confirmed that systems with microscopically reversible dynamics in locally quadratic potentials warm up faster than they cool down. This thermal relaxation asymmetry challenged the local-equilibrium paradigm valid near equilibrium. Because the intuition and proof hinged on the dynamics obeying detailed balance, it was not clear whether the asymmetry persists in systems with irreversible dynamics. To fill this gap, we here prove the relaxation asymmetry for systems driven out of equilibrium by a general linear drift. The asymmetry persists due to a non-trivial isomorphism between driven and reversible processes. Moreover, rotational motions emerge that, strikingly, occur in opposite directions during heating and cooling. This highlights that noisy systems do not relax by passing through local equilibria.

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arXiv2023

Global Speed Limit for Finite-Time Dynamical Phase Transition and Nonequilibrium Relaxation

Recent works unraveled an intriguing finite-time dynamical phase transition in the thermal relaxation of the mean field Curie-Weiss model. The phase transition reflects a sudden switch in the dynamics. Its existence in systems with a finite range of interaction, however, remained unclear. Here we demonstrate the dynamical phase transition for nearest-neighbor Ising systems on the square and Bethe lattices through extensive computer simulations and by analytical results. Combining large-deviation techniques and Bethe-Guggenheim theory we prove the existence of the dynamical phase transition for arbitrary quenches, including those within the two-phase region. Strikingly, for any given initial condition we prove and explain the existence of non-trivial speed limits for the dynamical phase transition and the relaxation of magnetization, which are fully corroborated by simulations of the microscopic Ising model but are absent in the mean field setting. Pair correlations, which are neglected in mean field theory and trivial in the Curie-Weiss model, account for kinetic constraints due to frustrated local configurations that give rise to a global speed limit.

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arXiv2023

Heating and Cooling are Fundamentally Asymmetric and Evolve Along Distinct Pathways

According to conventional wisdom, a system placed in an environment with a different temperature tends to relax to the temperature of the latter, mediated by the flows of heat and/or matter that are set solely by the temperature difference. It is becoming clear, however, that thermal relaxation is much more intricate when temperature changes push the system far from thermodynamic equilibrium. Interestingly, under such conditions heating was predicted to be faster than cooling, which we experimentally confirm using an optically trapped colloidal particle. More strikingly, we show with both experiments and theory that between any pair of temperatures, heating is not only faster than cooling but the respective processes in fact evolve along fundamentally distinct pathways, which we explain with a new theoretical framework we coin "thermal kinematics".

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arXiv2023

Thermodynamically Consistent Phase-Field Theory Including Nearest-Neighbor Pair Correlations Explains Failure of Mean-Field Reasoning

Most of our current understanding of phase separation is based on ideas that disregard correlaions. Here we illuminate unexpected effects of correlations on the structure and thermodynamics of interfaces and in turn phase separation, which are decisive in systems with strong interactions. Evaluating the continuum limit of the Ising model on the Bethe-Guggenheim level, we derive a Cahn-Hilliard free energy that takes into account pair correlations. For a one-dimensional interface in a strip geometry these are shown to give rise to an effective interface broadening at interaction strengths near and above the thermal energy, which is verified in the Ising model. Interface broadening is the result of an entropy-driven interface delocalization, which is not accounted for in the widely adopted mean field theory. Pair correlations are required for thermodynamic consistency as they enforce a thermodynamically optimal local configuration of defects and profoundly affect nucleation and spinodal decomposition at strong coupling.

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arXiv2023

Direct Route to Thermodynamic Uncertainty Relations and Their Saturation

Thermodynamic uncertainty relations (TURs) bound the dissipation in non-equilibrium systems from below by fluctuations of an observed current. Contrasting the elaborate techniques employed in existing proofs, we here prove TURs directly from the Langevin equation. This establishes the TUR as an inherent property of overdamped stochastic equations of motion. In addition, we extend the transient TUR to currents and densities with explicit time-dependence. By including current-density correlations we, moreover, derive a new sharpened TUR for transient dynamics. Our arguably simplest and most direct proof, together with the new generalizations, allows us to systematically determine conditions under which the different TURs saturate and thus allows for a more accurate thermodynamic inference. Finally we outline the direct proof also for Markov jump dynamics.

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arXiv2023

Feynman-Kac theory of time-integrated functionals: Itô versus functional calculus

The fluctuations of dynamical functionals such as the empirical density and current as well as heat, work and generalized currents in stochastic thermodynamics are usually studied within the Feynman-Kac tilting formalism, which in the Physics literature is typically derived by some form of Kramers-Moyal expansion, or in the Mathematical literature via the Cameron-Martin-Girsanov approach. Here we derive the Feynman-Kac theory for general additive dynamical functionals directly via Itô calculus and via functional calculus, where the latter result in fact appears to be new. Using Dyson series we then independently recapitulate recent results on steady-state (co)variances of general additive dynamical functionals derived recently in Dieball and Godec ({2022 \textit{Phys. Rev. Lett.}~\textbf{129} 140601}) and Dieball and Godec ({2022 \textit{Phys. Rev. Res.}~\textbf{4} 033243}). We hope for our work to put the different approaches to the statistics of dynamical functionals employed in the field on a common footing, and to illustrate more easily accessible ways to the tilting formalism.

cond-mat.stat-mech↗

arXiv2022

On correlations and fluctuations of time-averaged densities and currents with general time-dependence

We present technical results required for the description and understanding of correlations and fluctuations of the empirical density and current as well as diverse time-integrated and time-averaged thermodynamic currents of diffusion processes with a general time dependence on all time scales. In particular, we generalize the results from arXiv:2105.10483 (Phys. Rev. Lett., article in press), arXiv:2204.06553 (Phys. Rev. Research, article in press), and arXiv:2206.04034 to additive functionals with explicit time dependence and transient or non-ergodic overdamped diffusion. As an illustration we apply the results to two-dimensional harmonically confined overdamped diffusion in a rotational flow evolving from a non-stationary initial distribution.

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arXiv2022

Comment on "Inferring broken detailed balance in the absence of observable currents"

We present a simple biophysical example that invalidates the main conclusion of "Nat. Commun. 10, 3542 (2019)". Moreover, we explain that systems with one or more hidden states between at least one pair of observed states that give rise to non-instantaneous transition paths between these states also invalidate the main conclusion of the aforementioned work. This provides a flexible roadmap for constructing counterexamples. We hope for this comment to raise awareness of possibly hidden transition paths and of the importance of considering the microscopic origin of emerging non-Markovian (or Markovian) dynamics for thermodynamics.

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arXiv2022

Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space

We present general results on fluctuations and spatial correlations of the coarse-grained empirical density and current of Markovian diffusion in equilibrium or non-equilibrium steady states on all time scales. We unravel a deep connection between current fluctuations and generalized time-reversal symmetry, providing new insight into time-averaged observables. We highlight the essential role of coarse graining in space from mathematical, thermodynamical, and experimental points of view. Spatial coarse graining is required to uncover salient features of currents that break detailed balance, and a thermodynamically "optimal" coarse graining ensures the most precise inference of dissipation. Defined without coarse graining, the fluctuations of empirical density and current are proven to diverge on all time scales in dimensions higher than one, which has far-reaching consequences for the central-limit regime in continuous space. We apply the results to examples of irreversible diffusion. Our findings provide new intuition about time-averaged observables and allow for a more efficient analysis of single-molecule experiments.

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arXiv2022

Coarse Graining Empirical Densities and Currents in Continuous-Space Steady States

We present the conceptual and technical background required to describe and understand the correlations and fluctuations of the empirical density and current of steady-state diffusion processes on all time scales -- observables central to statistical mechanics and thermodynamics on the level of individual trajectories. We focus on the important and non-trivial effect of a spatial coarse graining. Making use of a generalized time-reversal symmetry we provide deeper insight about the physical meaning of fluctuations of the coarse-grained empirical density and current, and explain why a systematic variation of the coarse-graining scale offers an efficient method to infer bounds on a system's dissipation. Moreover, we discuss emerging symmetries in the statistics of the empirical density and current, and the statistics in the central-limit regime. More broadly our work promotes the application of stochastic calculus as a powerful direct alternative to Feynman-Kac theory and path-integral methods.

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arXiv2022

Faster uphill relaxation in thermodynamically equidistant temperature quenches

We uncover an unforeseen asymmetry in relaxation -- for a pair of thermodynamically equidistant temperature quenches, one from a lower and the other from a higher temperature, the relaxation at the ambient temperature is faster in case of the former. We demonstrate this finding on hand of two exactly solvable many-body systems relevant in the context of single-molecule and tracer-particle dynamics. We prove that near stable minima and for all quadratic energy landscapes it is a general phenomenon that also exists in a class of non-Markovian observables probed in single-molecule and particle-tracking experiments. The asymmetry is a general feature of reversible overdamped diffusive systems with smooth single-well potentials and occurs in multi-well landscapes when quenches disturb predominantly intra-well equilibria. Our findings may be relevant for the optimization of stochastic heat engines.

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arXiv2022

Violation of Local Detailed Balance Despite a Clear Time-Scale Separation

Integrating out fast degrees of freedom is known to yield, to a good approximation, memory-less, i.e. Markovian, dynamics. In the presence of such a time-scale separation local detailed balance is believed to emerge and to guarantee thermodynamic consistency arbitrarily far from equilibrium. Here we present a transparent example of a Markov model of a molecular motor where local detailed balance can be violated despite a clear time-scale separation and hence Markovian dynamics. Driving the system far from equilibrium can lead to a violation of local detailed balance against the driving force. We further show that local detailed balance can be restored, even in the presence of memory, if the coarse-graining is carried out as Milestoning. Our work establishes Milestoning not only as a kinetically but for the first time also as a thermodynamically consistent coarse-graining method. Our results are relevant as soon as individual transition paths are appreciable or can be resolved.

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