Time Irreversibility Research Articles

Evaluating Time Irreversibility Tests Using Geometric Brownian Motions with Stochastic Resetting

Evaluating Time Irreversibility Tests Using Geometric Brownian Motions with Stochastic Resetting

Time Irreversibility of Complex Time Series with Detrended Cross-Correlation Analysis Based on Visibility Graph

In this paper, we introduce detrended cross-correlation analysis (DCCA) method into visibility graph (VG) algorithm and propose VGDCCA method to reflect the time series irreversibility from a new perspective. The validity and reliability of the proposed VGDCCA method is supported by numerical simulations on synthesized short-term correlated chaotic systems and long-term correlated fractal processes, and by the empirical analysis on stock indices and traffic parameter. The VGDCCA planes suggest that autoregressive fractionally integrated moving average (ARFIMA) and fractional Gaussian noise (FGN) series show time reversible behavior, whatever the long-term correlation of the series is or however strong the persistence or anti-persistence of the series is. Meanwhile, Logistic map with [Formula: see text] and Hénon map show more time irreversible behaviors than those of ARFIMA, FGN series and other Logistic maps. It can be found that the relationship between cross-correlation of ingoing degree sequence and outgoing degree sequence for the simulated series with different parameters is consistent with the complexity and autocorrelation behavior in the corresponding definition of the time series. For the empirical analysis, VGDCCA method declares the similarity and dissimilarity between stock indices on time series irreversibility and captures the time irreversibility of traffic time series recorded by the detectors in different locations.

Irreversibility in belief dynamics: Unraveling the link to cognitive effort.

The relationship between time irreversibility in neuronal dynamics and cognitive effort is a subject of growing interest in the scientific literature. Although correlations between proxies of both concepts have been experimentally observed, the underlying precise linkage between them remains elusive. Here we investigate the case of learning in decision-making tasks; we do so by introducing a thermodynamically grounded metric-inspired by Landauer's principle-which connects time-irreversible information processing to energy consumption. Equipped with this metric, we investigate the role of macroscopic time-reversal symmetry breaking in belief dynamics for the case of an agent with finite sensitivity while performing a static two-armed bandit task-a standard setup in cognitive neuroscience. To gain insights into the belief dynamics, we analogize it to the dynamics of an active particle subject to state-dependent noise and living in a two-dimensional space. This mapping allows an analytical description of learning-induced biases. We deeply explore the case of Q-learning with forgetting the nonchosen option. In this case, learning-induced risk aversion is formally equivalent to standard thermophoresis, i.e., the net motion towards low-temperature regions. Finally, we quantify the irreversibility of belief dynamics in the steady state for different bandit configurations, sensitivity levels, and exploitative behavior. We found a strong correlation in high-sensitivity learning between heightened irreversibility in belief dynamics and improved decision-making outcomes. Notably, as the task's difficulty increases, a greater degree of irreversibility in belief dynamics becomes necessary for having superior performances; this explicitly unravels a plausible connection between time irreversibility and cognitive effort. In conclusion, our investigation reveals that irreversibility in belief dynamics bridges out-of-equilibrium statistical physics concepts and cognitive neuroscience. In decision-making contexts, this perspective offers insights into the notion of cognitive effort, suggesting a potential mechanism driving the evolution of living systems toward out-of-equilibrium structures.

Lagrangian Irreversibility and Energy Exchanges in Rotating-Stratified Turbulent Flows.

Turbulence in stratified and rotating turbulent flows is characterized by an interplay between waves and eddies, resulting in continuous exchanges between potential and kinetic energy. Here, we study how these processes affect the turbulent energy cascade from large to small scales, which manifests itself by an irreversible evolution of the relative kinetic energy between two tracer particles. We find that when r_{0}, the separation between particles, is below a characteristic length ℓ_{t}, potential energy is on average transferred to kinetic energy, reducing time irreversibility, and conversely when r_{0}>ℓ_{t}. Our Letter reveals that the scale ℓ_{t} coincides with the buoyancy length scale L_{B} over a broad range of configurations until a transition to a wave-dominated regime is reached.

Understanding underlying physical mechanism reveals early warning indicators and key elements for adaptive infections disease networks.

The study of infectious diseases holds significant scientific and societal importance, yet current research on the mechanisms of disease emergence and prediction methods still face challenging issues. This research uses the landscape and flux theoretical framework to reveal the non-equilibrium dynamics of adaptive infectious diseases and uncover its underlying physical mechanism. This allows the quantification of dynamics, characterizing the system with two basins of attraction determined by gradient and rotational flux forces. Quantification of entropy production rates provides insights into the system deviating from equilibrium and associated dissipative costs. The study identifies early warning indicators for the critical transition, emphasizing the advantage of observing time irreversibility from time series over theoretical entropy production and flux. The presence of rotational flux leads to an irreversible pathway between disease states. Through global sensitivity analysis, we identified the key factors influencing infectious diseases. In summary, this research offers valuable insights into infectious disease dynamics and presents a practical approach for predicting the onset of critical transition, addressing existing research gaps.

Transmission of waves and particles through the interface: Reversibility and coherence

We examine the transmission of quantum particles (phonons, electrons, and photons) across interfaces, identifying universal patterns in diverse physical scenarios. Starting with classical wave equations, we quantize them and derive kinetic equations. Those are matching conditions for the distribution functions of particles at the interface. We note the time irreversibility of the derived kinetic equations — an essential feature for accurately describing irreversible processes like heat transport. We identify the juncture in our derivation where the time symmetry of wave equations is disrupted, it is the assumption of the non-coherence of incident waves. Consequently, we infer that non-coherent transmission through the interface exhibits time irreversibility. We propose an experiment to validate this hypothesis.

Permutation time irreversibility in sleep electroencephalograms: Dependence on sleep stage and the effect of equal values.

Time irreversibility (TIR) refers to the manifestation of nonequilibrium brain activity influenced by various physiological conditions; however, the influence of sleep on electroencephalogram (EEG) TIR has not been sufficiently investigated. In this paper, a comprehensive study on permutation TIR (pTIR) of EEG data under different sleep stages is conducted. Two basic ordinal patterns (i.e., the original and amplitude permutations) are distinguished to simplify sleep EEGs, and then the influences of equal values and forbidden permutation on pTIR are elucidated. To detect pTIR of brain electric signals, five groups of EEGs in the awake, stages I, II, III, and rapid eye movement (REM) stages are collected from the public Polysomnographic Database in PhysioNet. Test results suggested that the pTIR of sleep EEGs significantly decreases as the sleep stage increases (p<0.001), with the awake and REM EEGs demonstrating greater differences than others. Comparative analysis and numerical simulations support the importance of equal values. Distribution of equal states, a simple quantification of amplitude fluctuations, significantly increases with the sleep stage (p<0.001). If these equalities are ignored, incorrect probabilistic differences may arise in the forward-backward and symmetric permutations of TIR, leading to contradictory results; moreover, the ascending and descending orders for symmetric permutations also lead different outcomes in sleep EEGs. Overall, pTIR in sleep EEGs contributes to our understanding of quantitative TIR and classification of sleep EEGs.

Global dynamics, thermodynamics and non-equilibrium origin of bifurcations for single neuron dynamics.

The understanding of neural excitability and oscillations in single neuron dynamics remains incomplete in terms of global stabilities and the underlying mechanisms for phase formation and associated phase transitions. In this study, we investigate the mechanism of single neuron excitability and spontaneous oscillations by analyzing the potential landscape and curlflux. The topological features of the landscape play a crucial role in assessing the stability of resting states and the robustness/coherence of oscillations. We analyze the excitation characteristics in Class I and Class II neurons and establish their relation to biological function. Our findings reveal that the average curlflux and associated entropy production exhibit significant changes near bifurcation or phase transition points. Moreover, the curlflux and entropy production offer insights into the dynamical and thermodynamical origins of nonequilibrium phase transitions and exhibit distinct behaviors in Class I and Class II neurons. Additionally, we quantify time irreversibility through the difference in cross-correlation functions in both forward and backward time, providing potential indicators for the emergence of nonequilibrium phase transitions in single neurons.

Quantifying nonequilibrium dynamics and thermodynamics of cell fate decision making in yeast under pheromone induction.

Cellular responses to pheromone in yeast can range from gene expression to morphological and physiological changes. While signaling pathways are well studied, the cell fate decision-making during cellular polar growth is still unclear. Quantifying these cellular behaviors and revealing the underlying physical mechanism remain a significant challenge. Here, we employed a hidden Markov chain model to quantify the dynamics of cellular morphological systems based on our experimentally observed time series. The resulting statistics generated a stability landscape for state attractors. By quantifying rotational fluxes as the non-equilibrium driving force that tends to disrupt the current attractor state, the dynamical origin of non-equilibrium phase transition from four cell morphological fates to a single dominant fate was identified. We revealed that higher chemical voltage differences induced by a high dose of pheromone resulted in higher chemical currents, which will trigger a greater net input and, thus, more degrees of the detailed balance breaking. By quantifying the thermodynamic cost of maintaining morphological state stability, we demonstrated that the flux-related entropy production rate provides a thermodynamic origin for the phase transition in non-equilibrium morphologies. Furthermore, we confirmed that the time irreversibility in time series provides a practical way to predict the non-equilibrium phase transition.

Irreversibility of symbolic time series: A cautionary tale.

Many empirical time series are genuinely symbolic: Examples range from link activation patterns in network science, to DNA coding or firing patterns in neuroscience, to cryptography or combinatorics on words. In some other contexts, the underlying time series is actually real valued, and symbolization is applied subsequently, as in symbolic dynamics of chaotic systems. Among several time series quantifiers, time series irreversibility-the difference between forward and backward statistics in stationary time series-is of great relevance. However, the irreversible character of symbolized time series is not always equivalent to the one of the underlying real-valued signal, leading to some misconceptions and confusion on interpretability. Such confusion is even bigger for binary time series-a classical way to encode chaotic trajectories via symbolic dynamics. In this paper we aim to clarify some usual misconceptions and provide theoretical grounding for the practical analysis-and interpretation-of time irreversibility in symbolic time series. We outline sources of irreversibility in stationary symbolic sequences coming from frequency asymmetries of nonpalindromic pairs which we enumerate, and prove that binary time series cannot show any irreversibility based on words of length m<4, thus discussing the implications and sources of confusion. We also study irreversibility in the context of symbolic dynamics, and clarify why these can be reversible even when the underlying dynamical system is not, such as the case of the fully chaotic logistic map.

Multiscale cross-sample entropy based on visibility graph for quantifying time series irreversibility

In this paper, we propose VGMCSE method to obtain multiscale time series irreversibility and gain more information from time irreversibility analysis. The validity of VGMCSE method is illustrated by numerical simulations on synthesized data and then VGMCSE method is applied on traffic time series to give better understanding about the traffic system from the view of time series irreversibility. By means of the VGMCSE planes for all the simulated time series, it can be found that ARFIMA and FGN series are all time reversible, while Logistic map & Hénon map are time irreversible. The simulated series can be classified into two groups: (1) ARFIMA & FGN, (2) Logistic map & Hénon map by their time series irreversibility. It can be found that the relationship between asynchrony of ingoing degree sequence and outgoing degree sequence for the simulated series with different parameter is consistent with the complexity and autocorrelation behavior in the corresponding definition of the time series. However, it can be revealed that whether the series is long-term correlated or no matter how strong the persistence or anti-persistence is, the ARFIMA and FGN series are all time reversible, indicating time series irreversibility might have no direct connection with long-range dependence and stationarity of series. For the empirical analysis, the traffic time series recorded by detectors can be classified into three groups: (1) detector 2037, 2038, (2) detector 3055, (3) detector 2036, 2040, 3054, 3056, 3057, 4051, 4052, suggesting that there is more similar time irreversible behavior for speed and volume time series recorded by detectors with nearer positions, while the traffic time series of some special locations present different time irreversible behavior and these locations should be paid more attention and enhanced monitoring. VGMCSE method can not only show the asynchrony of ingoing degree sequence and outgoing degree sequence, but also detect the time series irreversibility for time series of complex system.

Coherent structures at the origin of time irreversibility in wall turbulence

Time irreversibility is a distinctive feature of non-equilibrium phenomena such as turbulent flows, where irreversibility is mainly associated with an energy cascade process. The connection between time irreversibility and coherent motions in wall turbulence, however, has not been investigated yet. An Eulerian, multiscale analysis of time irreversibility in wall-bounded turbulence is proposed in this study, which differs from previous works relying on a Lagrangian approach and mainly focusing on homogeneous turbulence. Outcomes reveal a strong connection between irreversibility levels and coherent structures in both turbulent channel and boundary layer flows. In the near-wall region, irreversibility is directly related to the inner spectral peak originating from small-scale turbulent structures in the buffer layer. Conversely, stronger irreversibility is found in correspondence to the outer spectral peak originating from larger turbulent flow scales far from the wall. Our results represent a first effort to characterize Eulerian TI in wall-bounded turbulent flows, thus paving the way for further developments in wall-turbulence modeling and control accounting for broken temporal symmetry.

Continuous ordinal patterns: Creating a bridge between ordinal analysis and deep learning.

We introduce a generalization of the celebrated ordinal pattern approach for the analysis of time series, in which these are evaluated in terms of their distance to ordinal patterns defined in a continuous way. This allows us to naturally incorporate information about the local amplitude of the data and to optimize the ordinal pattern(s) to the problem under study. This last element represents a novel bridge between standard ordinal analysis and deep learning, allowing the achievement of results comparable to the latter in real-world classification problems while also retaining the conceptual simplicity, computational efficiency, and easy interpretability of the former. We test this through the use of synthetic time series, generated by standard chaotic maps and dynamical models, data sets representing brain activity in health and schizophrenia, and the dynamics of delays in the European air transport system. We further show how the continuous ordinal patterns can be used to assess other aspects of the dynamics, like time irreversibility.

Non-equilibrium early-warning signals for critical transitions in ecological systems

Complex systems can exhibit sudden transitions or regime shifts from one stable state to another, typically referred to as critical transitions. It becomes a great challenge to identify a robust warning sufficiently early that action can be taken to avert a regime shift. We employ landscape-flux theory from nonequilibrium statistical mechanics as a general framework to quantify the global stability of ecological systems and provide warning signals for critical transitions. We quantify the average flux as the nonequilibrium driving force and the dynamical origin of the nonequilibrium transition while the entropy production rate as the nonequilibrium thermodynamic cost and thermodynamic origin of the nonequilibrium transition. Average flux, entropy production, nonequilibrium free energy, and time irreversibility quantified by the difference in cross-correlation functions forward and backward in time can serve as early warning signals for critical transitions much earlier than other conventional predictors. We utilize a classical shallow lake model as an exemplar for our early warning prediction. Our proposed method is general and can be readily applied to assess the resilience of many other ecological systems. The early warning signals proposed here can potentially predict critical transitions earlier than established methods and perhaps even sufficiently early to avert catastrophic shifts.

Weather pattern dynamics over western Europe under climate change: predictability, information entropy and production

Abstract. The impact of climate change on weather pattern dynamics over the North Atlantic is explored through the lens of the information theory of forced dissipative dynamical systems. The predictability problem is first tackled by investigating the evolution of block entropies on observational time series of weather patterns produced by the Met Office, which reveals that predictability is increasing as a function of time in the observations during the 19th century and beginning of the 20th century, while the trend is reversed at the end of the 20th century and beginning of the 21st century. This feature is also investigated in the 15-member ensemble of the UK Met Office CMIP5 model for the 20th and 21st centuries under two climate change scenarios, revealing a wide range of possible evolutions depending on the realization considered, with an overall decrease in predictability in the 21st century for both scenarios. Lower bounds of the information entropy production are also extracted, providing information on the degree of time asymmetry and irreversibility of the dynamics. The analysis of the UK Met Office model runs suggests that the information entropy production will increase by the end of the 21st century, by a factor of 10 % in the Representative Carbon Pathway RCP2.6 scenario and a factor of 30 %–40 % in the RCP8.5 one, as compared to the beginning of the 20th century. This allows one to make the conjecture that the degree of irreversibility is increasing, and hence heat production and dissipation will also increase under climate change, corroborating earlier findings based on the analysis of the thermodynamic entropy production.

On time irreversibility of generalized Hassani kinematics

On time irreversibility of generalized Hassani kinematics

Is Climate Change Time-Reversible?

This paper proposes strategies to detect time reversibility in stationary stochastic processes by using the properties of mixed causal and noncausal models. It shows that they can also be used for non-stationary processes when the trend component is computed with the Hodrick–Prescott filter rendering a time-reversible closed-form solution. This paper also links the concept of an environmental tipping point to the statistical property of time irreversibility and assesses fourteen climate indicators. We find evidence of time irreversibility in greenhouse gas emissions, global temperature, global sea levels, sea ice area, and some natural oscillation indices. While not conclusive, our findings urge the implementation of correction policies to avoid the worst consequences of climate change and not miss the opportunity window, which might still be available, despite closing quickly.

Inference of time irreversibility from incomplete information: Linear systems and its pitfalls

Data from experiments and theoretical arguments are the two pillars sustaining the job of modeling physical systems through inference. In order to solve the inference problem, the data should satisfy certain conditions that depend also upon the particular questions addressed in a research. Here we focus on the characterization of systems in terms of a distance from equilibrium, typically the entropy production (time-reversal asymmetry) or the violation of the Kubo fluctuation-dissipation relation. We show how general, counterintuitive and negative for inference, is the problem of the impossibility to estimate the distance from equilibrium using a series of scalar data which have a Gaussian statistics. This impossibility occurs also when the data are correlated in time, and that is the most interesting case because it usually stems from a multi-dimensional linear Markovian system where there are many timescales associated to different variables and, possibly, thermal baths. Observing a single variable (or a linear combination of variables) results in a one-dimensional process which is always indistinguishable from an equilibrium one (unless a perturbation-response experiment is available). In a setting where only data analysis (and not new experiments) is allowed, we propose as a way out the combined use of different series of data acquired with different parameters. This strategy works when there is a sufficient knowledge of the connection between experimental parameters and model parameters. We also briefly discuss how such results emerge, similarly, in the context of Markov chains within certain coarse-graining schemes. Our conclusion is that the distance from equilibrium is related to quite a fine knowledge of the full phase space, and therefore typically hard to approximate in real experiments.

Time irreversibility analysis and abnormality detection based on Riemannian geometry for complex time series

Time irreversibility (TIR) is one of the basic properties of nonlinear systems, and it can be used as an effective way to explore the nonlinear complexity of dynamic systems. In this paper, we propose the TIR measure algorithm based on Riemannian geometry and apply this algorithm to abnormality detection tasks. The core idea is to calculate the positive definite covariance matrices of the forward sequence and its inverse sequence based on the theories of sliding window and phase space reconstruction, and compute the affine invariant Riemannian metric (AIRM) between them to characterize the TIR of the time series. The advantage of this algorithm is that the framework based on Riemannian geometry can more effectively use the spatial information of time series. In addition, compared with the traditional methods, the new method is suitable for nonstationary complex systems, which introduces a sliding window to make subsequences satisfy weak stationary conditions to measure local time irreversibility. The simulated and surrogate data are used to verify the effectiveness of the algorithm. Finally, we apply the algorithm to empirical analysis. The results show that, the algorithm detects the financial crisis period and stable period of the stock markets in the analysis of the financial system, and the loss degree of TIR of physiologic signals of different types of cardiac patients is detected in the study of physiologic signals. In the research of Parkinson’s gait, we verify that the walker is an effective tool to improve the gait of early Parkinson’s patients through statistical tests.

Comparative analysis of time irreversibility and amplitude irreversibility based on joint permutation

Although time irreversibility (TIR) and amplitude irreversibility (AIR) are relevant concepts for nonequilibrium analysis, their association has received little attention. This paper conducts a systematic comparative analysis of the relationship between TIR and AIR based on statistical descriptions and numerical simulations. To simplify the quantification of TIR and AIR, the amplitude permutation and global information of the associated vector are combined to produce a joint probability estimation. Chaotic logistic, Henon, and Lorenz series are generated to evaluate TIR and AIR according to surrogate theory, and the distributions of joint permutations for these model series are measured to compare the degree of TIR and AIR. The joint permutation TIR and AIR are then used to investigate nonequilibrium pathological features in epileptic electroencephalography data. Test results suggest that epileptic brain electrical activities, particular those during the onset of seizure, manifest higher nonequilibrium characteristics. According to the statistical definitions and targeted pairs of joint permutations in the chaotic model data, TIR and AIR are fundamentally different nonequilibrium descriptors from time- and amplitude-reversibility, respectively, and thus require different forms of numerical analysis. At the same time, TIR and AIR both provide measures for fluctuation theorems associated with nonequilibrium processes, and have similar probabilistic differences in the pairs of joint permutations and consistent outcomes when used to analyze both the model series and real-world signals. Overall, comparative analysis of TIR and AIR contributes to our understanding of nonequilibrium features and broadens the scope of quantitative nonequilibrium measures. Additionally, the construction of joint permutations contributes to the development of symbolic time series analysis.