Time Irreversibility Research Articles

Assessment of time irreversibility in a time series using visibility graphs.

In this paper, we studied the time-domain irreversibility of time series, which is a fundamental property of systems in a nonequilibrium state. We analyzed a subgroup of the databases provided by University of Rochester, namely from the THEW Project. Our data consists of LQTS (Long QT Syndrome) patients and healthy persons. LQTS may be associated with an increased risk of sudden cardiac death (SCD), which is still a big clinical problem. ECG-based artificial intelligence methods can identify sudden cardiac death with a high accuracy. It follows that heart rate variability contains information about the possibility of SCD, which may be extracted, provided that appropriate methods are developed for this purpose. Our aim was to assess the complexity of both groups using visibility graph (VG) methods. Multivariate analysis of connection patterns of graphs built from time series was performed using multiplex visibility graph methods. For univariate time series, time irreversibility of the ECG interval QT of patients with LQTS was lower than for the healthy. However, we did not observe statistically significant difference in the comparison of RR intervals time series of the two groups studied. The connection patterns retrieved from multiplex VGs have more similarity with each other in the case of LQTS patients. This observation may be used to develop better methods for SCD risk stratification.

Eulerian vs Lagrangian Irreversibility in an Experimental Turbulent Swirling Flow.

In a turbulent fluid, the time-reversal symmetry is explicitly broken by viscosity, and spontaneously broken in the inviscid limit. Recently, Drivas [J. Nonlinear Sci. 29, 65 (2019).JNSCEK0938-897410.1007/s00332-018-9476-8] proved the equivalence of two different local indicators of time irreversibility: (i)an Eulerian one, based on regularity properties of the velocity field [Duchon and Robert, Nonlinearity 13, 249 (2000).NONLE50951-771510.1088/0951-7715/13/1/312]; (ii)a Lagrangian one, based on symmetry properties of the trajectories under time reversal [Jucha et al., Phys. Rev. Lett. 113, 054501 (2014).PRLTAO0031-900710.1103/PhysRevLett.113.054501]. We test this equivalence in a turbulent Von Kármán experiment at a resolution of the order of the Kolmogorov scale using a high resolution 4D-PTV technique. We use the equivalence to perform the first joined Eulerian-Lagrangian exploration of the dynamics leading to time irreversibility, and find that it is linked with vortex interaction, suggesting a link between irreversibility and singularity.

Velocity-like maximum polarization: Irreversibility and quantum measurements

The polarization emerging in the subsequent scattering processes can never exceed $1$ which corresponds to the fully polarized pure state. This property is shown to be provided by the addition rule similar to that for relativistic velocities never exceeding the speed of light. The cases of spin $1/2$ and $1$ are considered. The photon linear polarization in Thomson scattering is monotonically increasing. This directness is shown to be a consequence of spin measurement procedure and may be the particular example of ithe anticipated relation between quantum measurement and time irreversibility. The emergent polarization may be considered as a case of opposing time's arrows corresponding to microscopic (spin) and macroscopic (momentum) degrees of freedom, respectively.

Use of streamflow indices to identify the catchment drivers of hydrographs

Abstract. Time irreversibility or temporal asymmetry refers to the steeper ascending and gradual descending parts of a streamflow hydrograph. The primary goal of this study is to bring out the distinction between streamflow indices directly linked with rising limbs and falling limbs and to explore their utility in uncovering processes associated with the steeper ascending and gradual descending limbs of the hydrograph within the time-irreversibility paradigm. Different streamflow indices are correlated with the rising and falling limbs and the catchment attributes. The key attributes governing rising and falling limbs are then identified. The contribution of the work is on differentiating hydrographs by their time irreversibility features and offering an alternative way to recognize primary drivers of streamflow hydrographs. A series of spatial maps describing the streamflow indices and their regional variability in the Contiguous United States (CONUS) is introduced here. These indices complement the catchment attributes provided earlier (Addor et al., 2017) for the CAMELS data set. The findings of the study revealed that the elevation, fraction of precipitation falling as snow and depth to bedrock mainly characterize the rising limb density, whereas the aridity and frequency of precipitation influence the rising limb scale parameter. Moreover, the rising limb shape parameter is primarily influenced by the forest fraction, the fraction of precipitation falling as snow, mean slope, mean elevation, sand fraction, and precipitation frequency. It is noted that falling limb density is mainly governed by climate indices, mean elevation, and the fraction of precipitation falling as snow; however, the recession coefficients are controlled by mean elevation, mean slope, clay, the fraction of precipitation falling as snow, forest fraction, and sand fraction.

Magnetic energy spectrum produced by turbulent dynamo: Effect of time irreversibility

We consider the kinematic stage of evolution of magnetic field advected by turbulent hydrodynamic flow. We use a generalization of the Kazantsev–Kraichnan model to investigate time irreversible flows. In the viscous range of scales, the infinite-time limit of the spectrum is a power law, but its slope is more flat than that predicted by the Kazantsev model. This result agrees with numerical simulations. The rate of magnetic energy growth is slower than that in the time-symmetric case. We show that for high magnetic Prandtl turbulent plasma, the formation of the power-law spectrum shape takes very long time and may never happen because of the nonlinearity. We propose another ansatz to describe the spectrum shape at finite time.

Irreversibility in linear systems with colored noise.

Time irreversibility is a distinctive feature of nonequilibrium dynamics and several measures of irreversibility have been introduced to assess the distance from thermal equilibrium of a stochastically driven system. While the dynamical noise is often approximated as white, in many real applications the time correlations of the random forces can actually be significantly long-lived compared to the relaxation times of the driven system. We analyze the effects of temporal correlations in the noise on commonly used measures of irreversibility and demonstrate how the theoretical framework for white-noise-driven systems naturally generalizes to the case of colored noise. Specifically, we express the autocorrelation function, the area enclosing rates, and mean phase space velocity in terms of solutions of a Lyapunov equation and in terms of their white-noise limit values.

Time irreversibility in active matter, from micro to macro

Active matter encompasses systems whose individual constituents dissipate energy to exert propelling forces on their environment. These systems exhibit dynamical phenomena with no counterpart in passive systems. In this Review, we disentangle the respective roles of the arrow of time and the non-Boltzmann nature of steady-state fluctuations in this rich phenomenology. We show that effective, time-reversible descriptions of active systems may be found at all scales and discuss how interactions, either between constituents or with external operators, may reveal the nonequilibrium nature of the microscopic source of energy. At a time when engineering active materials appears to be becoming possible, we argue that methods stemming from equilibrium statistical mechanics may guide the design of new active materials. Much of the rich phenomenology of active matter can be traced back to violations of time-reversal symmetry and departure from Boltzmann statistics. This Review disentangles these nonequilibrium signatures for interacting and dilute systems, in the presence of obstacles and external potentials.

Investigation on the Prediction of Cardiovascular Events Based on Multi-Scale Time Irreversibility Analysis

Investigation of the risk factors associated with cardiovascular disease (CVD) plays an important part in the prevention and treatment of CVD. This study investigated whether alteration in the multi-scale time irreversibility of sleeping heart rate variability (HRV) was a risk factor for cardiovascular events. The D-value, based on analysis of multi-scale increments in HRV series, was used as the measurement of time irreversibility. Eighty-four subjects from an open-access database (i.e., the Sleep Heart Health Study) were included in this study. None of them had any CVD history at baseline; 42 subjects had cardiovascular events within 1 year after baseline polysomnography and were classed as the CVD group, and the other 42 subjects in the non-CVD group were age matched with those in the CVD group and had no cardiovascular events during the 15-year follow-up period. We compared D-values of sleeping HRV between the CVD and non-CVD groups and found that the D-values of the CVD group were significantly lower than those of the non-CVD group on all 10 scales, even after adjusting for gender and body mass index. Moreover, we investigated the performance of a machine learning model to classify CVD and non-CVD subjects. The model, which was fed with a feature space based on the D-values on 10 scales and trained by a random forest algorithm, achieved an accuracy of 80.8% and a positive prediction rate of 86.7%. These results suggest that the decreased time irreversibility of sleeping HRV is an independent predictor of cardiovascular events that could be used to assist the intelligent prediction of cardiovascular events.

Measuring the Topological Time Irreversibility of Time Series With the Degree-Vector-Based Visibility Graph Method

Time irreversibility of a time series, which can be defined as the variance of properties under the time-reversal transformation, is a cardinal property of non-equilibrium systems and is associated with predictability in the study of financial time series. Recent pieces of literature have proposed the visibility-graph-based approaches that specifically refer to topological properties of the network mapped from a time series, with which one can quantify different degrees of time irreversibility within the sets of statistically time-asymmetric series. However, all these studies have inadequacies in capturing the time irreversibility of some important classes of time series. Here, we extend the visibility-graph-based method by introducing a degree vector associated with network nodes to represent the characteristic patterns of the index motion. The newly proposed method is parameter-free and temporally local. The validation to canonical synthetic time series, in the aspect of time (ir)reversibility, illustrates that our method can differentiate a non-Markovian additive random walk from an unbiased Markovian walk, as well as a GARCH time series from an unbiased multiplicative random walk. We further apply the method to the real-world financial time series and find that the price motions occasionally equip much higher time irreversibility than the calibrated GARCH model does.

Algorithmic Approaches for Assessing Irreversibility in Time Series: Review and Comparison.

The assessment of time irreversibility, i.e., of the lack of invariance of the statistical properties of a system under the operation of time reversal, is a topic steadily gaining attention within the research community. Irreversible dynamics have been found in many real-world systems, with alterations being connected to, for instance, pathologies in the human brain, heart and gait, or to inefficiencies in financial markets. Assessing irreversibility in time series is not an easy task, due to its many aetiologies and to the different ways it manifests in data. It is thus not surprising that several numerical methods have been proposed in the last decades, based on different principles and with different applications in mind. In this contribution we review the most important algorithmic solutions that have been proposed to test the irreversibility of time series, their underlying hypotheses, computational and practical limitations, and their comparative performance. We further provide an open-source software library that includes all tests here considered. As a final point, we show that “one size does not fit all”, as tests yield complementary, and sometimes conflicting views to the problem; and discuss some future research avenues.

Assessing time series irreversibility through micro-scale trends.

Time irreversibility, defined as the lack of invariance of the statistical properties of a system or time series under the operation of time reversal, has received increasing attention during the last few decades, thanks to the information it provides about the mechanisms underlying the observed dynamics. Following the need of analyzing real-world time series, many irreversibility metrics and tests have been proposed, each one associated with different requirements in terms of, e.g., minimum time series length or computational cost. We here build upon previously proposed tests based on the concept of permutation patterns but deviating from them through the inclusion of information about the amplitude of the signal and how this evolves over time. We show, by means of synthetic time series, that the results yielded by this method are complementary to the ones obtained by using permutation patterns alone, thus suggesting that "one irreversibility metric does not fit all." We further apply the proposed metric to the analysis of two real-world data sets.

Optical response of laser-driven charge-transfer complex described by Holstein-Hubbard model coupled to heat baths: Hierarchical equations of motion approach.

We investigate the optical response of a charge-transfer complex in a condensed phase driven by an external laser field. Our model includes an instantaneous short-range Coulomb interaction and a local optical vibrational mode described by the Holstein-Hubbard (HH) model. Although characterization of the HH model for a bulk system has typically been conducted using a complex phase diagram, this approach is not sufficient for investigations of dynamical behavior at finite temperature, in particular for studies of nonlinear optical properties, where the time irreversibility of the dynamics that arises from the environment becomes significant. We therefore include heat baths with infinite heat capacity in the model to introduce thermal effects characterized by fluctuation and dissipation to the system dynamics. By reducing the number of degrees of freedom of the heat baths, we derive numerically "exact" hierarchical equations of motion for the reduced density matrix of the HH system. As demonstrations, we calculate the optical response of the system in two- and four-site cases under external electric fields. The results indicate that the effective strength of the system-bath coupling becomes large as the number of sites increases. Excitation of electrons promotes the conductivity when the Coulomb repulsion is equivalent to or dominates the electron-phonon coupling, whereas excitation of optical vibrations always suppresses the conductivity.

Quantifying entropy production in active fluctuations of the hair-cell bundle from time irreversibility and uncertainty relations

We introduce lower bounds for the rate of entropy production of an active stochastic process by quantifying the irreversibility of stochastic traces obtained from mesoscopic degrees of freedom. Our measures of irreversibility reveal signatures of time’s arrow and provide bounds for entropy production even in the case of active fluctuations that have no drift. We apply these irreversibility measures to experimental recordings of spontaneous hair-bundle oscillations in mechanosensory hair cells from the ear of the bullfrog. By analyzing the fluctuations of only the tip position of hair bundles, we reveal irreversibility in active oscillations and estimate an associated rate of entropy production of at least ∼3k B/s, on average. Applying thermodynamic uncertainty relations, we predict that measuring both the tip position of the hair bundle and the mechano-electrical transduction current that enters the hair cell leads to tighter lower bounds for the rate of entropy production, up to ∼103 k B/s in the oscillatory regime.

Landscape-Flux Framework for Nonequilibrium Dynamics and Thermodynamics of Open Hamiltonian Systems Coupled to Multiple Heat Baths.

We establish a nonequilibrium dynamic and thermodynamic formalism in the landscape-flux framework for open Hamiltonian systems in contact with multiple heat baths governed by stochastic dynamics. To systematically characterize nonequilibrium steady states, the nonequilibrium trinity construct is developed, which consists of detailed balance breaking, nonequilibrium potential landscape, and irreversible probability flux. We demonstrate that the temperature difference of the heat baths is the physical origin of detailed balance breaking, which generates the nonequilibrium potential landscape characterizing the nonequilibrium statistics and creates the irreversible probability flux signifying time irreversibility, with the latter two aspects closely connected. It is shown that the stochastic dynamics of the system can be formulated in the landscape-flux form, where the reversible force drives the conservative Hamiltonian dynamics, the irreversible force consisting of a landscape gradient force and an irreversible flux force drives the dissipative dynamics, and the stochastic force adds random fluctuations to the dynamics. The possible connection of the nonequilibrium trinity construct to nonequilibrium phase transitions is also suggested. A set of nonequilibrium thermodynamic equations, applicable to both nonequilibrium steady states and transient relaxation processes, is constructed. We find that an additional thermodynamic quantity, named the mixing entropy production rate, enters the nonequilibrium thermodynamic equations. It arises from the interplay between detailed balance breaking and transient relaxation, and it also relies on the conservative dynamics. At the nonequilibrium steady state, the heat flow, entropy flow, and entropy production are demonstrated to be thermodynamic manifestations of the nonequilibrium trinity construct. The general nonequilibrium formalism is applied to a class of solvable systems consisting of coupled harmonic oscillators. A more specific example of two harmonic oscillators coupled to two heat baths is worked out in detail. The example may facilitate connection with experiments.

Increase in entropy and time irreversibility in Hamiltonian dynamics

Increase in entropy and time irreversibility in Hamiltonian dynamics

Increase in entropy and time irreversibility in Hamiltonian dynamics

Построена модель гамильтоновой полевой теории, объединяющей гидродинамику и термодинамику. В этой модели в качестве уравнений Гамильтона фигурируют уравнение непрерывности и уравнение Эйлера для потенциального течения, а в качестве уравнений связей второго рода - уравнения состояния (или эквивалентные им уравнения Гиббса). Редуцированная на поверхность связей второго рода плотность функции Гамильтона является суммой плотностей кинетической и потенциальной энергий, причем в качестве потенциальной энергии выступает свободная энергия. На поверхности связей второго рода возникает естественная симплектическая структура и канонические переменные, функциями которых являются все физические переменные. В частности, с точки зрения гамильтонова формализма энтропия интерпретируется как обобщенная скорость - множитель Лагранжа при соответствующей связи второго рода, выражающей температуру как функцию канонических переменных на последнем этапе редукции. На последнем этапе этот множитель выражается через канонические переменные, в результате чего возникает нетривиальное уравнение движения для энтропии. Чтобы продвинуться дальше, следует еще более конкретизировать модель, фиксировав зависимость удельной свободной энергии от своих аргументов. Выбирается простейший нетривиальный вариант - одноатомный газ Ван-дер-Ваальса, атомы которого находятся в основном состоянии. Канонические уравнения Гамильтона позволяют вычислить скорость изменения энтропии этой динамической системы. Для физически интересной ситуации, когда эволюция системы приводит к равновесию, энтропия и скорость ее изменения являются функционалами от решения динамических уравнений для плотности. Численное решение этих уравнений дает монотонный рост энтропии (для конечного времени эволюции). Для нахождения асимптотики по времени уравнения можно линеаризовать; для асимптотической эволюции отклонения плотности от равновесного значения получается не гиперболическое, а эллиптическое уравнение с "неправильным" знаком аналога квадрата скорости звука. Тем самым обратимость решения во времени теряется.

Unifying deterministic and stochastic ecological dynamics via a landscape-flux approach

The frequency distributions can characterize the population-potential landscape related to the stability of ecological states. We illustrate the practical utility of this approach by analyzing a forest-savanna model. Savanna and forest states coexist under certain conditions, consistent with past theoretical work and empirical observations. However, a grassland state, unseen in the corresponding deterministic model, emerges as an alternative quasi-stable state under fluctuations, providing a theoretical basis for the appearance of widespread grasslands in some empirical analyses. The ecological dynamics are determined by both the population-potential landscape gradient and the steady-state probability flux. The flux quantifies the net input/output to the ecological system and therefore the degree of nonequilibriumness. Landscape and flux together determine the transitions between stable states characterized by dominant paths and switching rates. The intrinsic potential landscape admits a Lyapunov function, which provides a quantitative measure of global stability. We find that the average flux, entropy production rate, and free energy have significant changes near bifurcations under both finite and zero fluctuation. These may provide both dynamical and thermodynamic origins of the bifurcations. We identified the variances in observed frequency time traces, fluctuations, and time irreversibility as kinematic measures for bifurcations. This framework opens the way to characterize ecological systems globally, to uncover how they change among states, and to quantify the emergence of quasi-stable states under stochastic fluctuations.

Behavioral discrimination and time-series phenotyping of birdsong performance.

Variation in the acoustic structure of vocal signals is important to communicate social information. However, relatively little is known about the features that receivers extract to decipher relevant social information. Here, we took an expansive, bottom-up approach to delineate the feature space that could be important for processing social information in zebra finch song. Using operant techniques, we discovered that female zebra finches can consistently discriminate brief song phrases (“motifs”) from different social contexts. We then applied machine learning algorithms to classify motifs based on thousands of time-series features and to uncover acoustic features for motif discrimination. In addition to highlighting classic acoustic features, the resulting algorithm revealed novel features for song discrimination, for example, measures of time irreversibility (i.e., the degree to which the statistical properties of the actual and time-reversed signal differ). Moreover, the algorithm accurately predicted female performance on individual motif exemplars. These data underscore and expand the promise of broad time-series phenotyping to acoustic analyses and social decision-making.

Variations of Time Irreversibility of Heart Rate Variability Under Normobaric Hypoxic Exposure.

In the field of biomedicine, time irreversibility is used to describe how imbalanced and asymmetric biological signals are. As an important feature of signals, the direction of time is always ignored. To find out the variation regularity of time irreversibility of heart rate variability (HRV) in the initial stage of hypoxic exposure, the present study implemented 2 h acute normobaric hypoxic exposure on six young subjects who have no plateau or hypoxia experiences; oxygen concentration was set as 12.9%. Electrocardiogram (ECG) signals were recorded in the whole process and RR interval sequences were extracted. Mathematical operations were executed to transform the difference of adjacent RR intervals into proportion and distance with delay time to conduct time irreversibility analysis of HRV. The same calculating method was implemented on six items randomly picked out from the MIT-BIH normal sinus rhythm database as a control group. Results show that variation of time irreversibility of HRV in a hypoxic environment is different from that in a normoxic environment, time irreversibility indices of a hypoxic group decreases continually at a delay time of 1 and 2, and indices curves of time irreversibility gradually tend to be steady and gather with each other at a delay time of 3 or 4. The control group shows no consistent tendency no matter what the delay time is in the range of 1–4. Our study indicates that in short-time hypoxic exposure, as hypoxic time goes by, regulation of the cardiovascular autonomic nervous system weakens; regulation times and intensity of sympathetic and parasympathetic nerves tend to be equal.

On the time irreversibility of compressible turbulence reflected by particles of various inertias

Time irreversibility of compressible homogeneous isotropic turbulence (HIT) is investigated from a Lagrangian point of view and single-particle statistics. For this purpose, direct numerical simulation (DNS) is implemented for compressible HIT at Taylor-mircoscale Reynolds number Reλ∼100 and turbulent Mach number Mt up to 1.01, in which tracers and inertial particles in a wide Stokes number (St) range are instantaneously tracked with time. The statistics of instantaneous power of particles corroborates that the violation of detailed balance of turbulence in compressible HIT is much stronger than in incompressible HIT. It turns out that the third moment of dimensionless instantaneous power (Ir) of tracers scales as Mt4. A possible explanation based on Kolmogorov-like argument proves to be plausible due to the lacks of direct verification and generality for other moments of the power. A further analysis from an Eulerian point of view suggests that the underlying mechanism for time irreversibility of highly compressible turbulence is quite different from that for weakly compressible or incompressible turbulence. For inertial particles, the moments of instantaneous power are suggested to scale as St−2n/3 at relatively large St numbers, and be dependent only on Mach number or Reynolds number at the small-St number end, which are manifested by the present numerical data. It is further shown that the empirical Mt4 scaling of Ir also approximately applies to various inertial particles, but only at high Mt numbers due to the diminishing effect of compressibility to the low-Mach number end. The time irreversibility announced by the Lagrangian statistical properties of particles of different inertias is shown to be highly associated with their responses to the vortex and shocklet structures in compressible turbulence.