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arxiv: 2511.15991 · v1 · submitted 2025-11-20 · ⚛️ physics.data-an · nlin.CD

Identifying statistical indicators of temporal asymmetry using a data-driven approach

Teresa Dalle Nogare , Ben D. Fulcher This is my paper

Pith reviewed 2026-05-17 21:17 UTC · model grok-4.3

classification ⚛️ physics.data-an nlin.CD
keywords time irreversibilitytemporal asymmetrytime-series statisticsdata-driven comparisonirreversible dynamicstime-reversibility metricssymbolic sequencesautocorrelation functions
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The pith

No single statistic detects time irreversibility across all systems, but a suitable one exists for each system tested.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper evaluates more than 6000 time-series summary statistics drawn from the literature on their power to tell whether a process looks the same forward and backward in time. Using data simulated from 35 different irreversible systems, it finds that every system can be correctly flagged as irreversible by at least one well-chosen statistic, yet no statistic succeeds for every system. Readers care because many real-world processes in physics, biology and engineering are irreversible, and the right measure can reveal dissipation or other mechanisms without assuming a specific model. The comparison singles out three promising families: time-asymmetric generalized autocorrelations, symbolic-sequence encodings, and forecasting-based quantities. The results imply that analysts should match the statistic to the particular form of irreversibility rather than expect one tool to work universally.

Core claim

By evaluating over 6000 time-series summary statistics on 35 diverse irreversible systems, the work shows that all irreversible systems studied could be accurately distinguished by a well-chosen time-series statistic, but no single statistic could accurately index the statistical form of irreversibility for all irreversible systems. This challenges the assumption that a given time-reversibility statistic will capture time reversibility in general and underscores the importance of tailoring statistical approaches to the time-reversal characteristics of a given system.

What carries the argument

Large-scale data-driven comparison of time-series summary statistics, with emphasis on time-asymmetric generalized autocorrelation functions, symbolic sequences, and forecasting-related methods.

If this is right

  • Time-asymmetric forms of generalized autocorrelation functions effectively distinguish certain classes of irreversible dynamics.
  • Symbolic-sequence encodings provide strong detection power for other forms of temporal asymmetry.
  • Forecasting-related statistics also succeed on particular irreversible systems.
  • The comparison supplies a unified view of the algorithmic structures that quantify irreversibility from data.
  • Patterns in time series can be more reliably linked to the underlying mechanisms that generate them.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Analysts working with real data may need to test several candidate statistics rather than adopt a single default measure.
  • The simulation-based findings could be checked by applying the same statistics to experimental recordings from known irreversible physical or biological systems.
  • Ensemble or adaptive methods that combine statistics from the highlighted families might cover a wider range of irreversibility types than any one statistic alone.
  • The results suggest a practical route for connecting observed time asymmetry to entropy production or other nonequilibrium signatures without presupposing a model.

Load-bearing premise

The 35 simulated systems capture a sufficiently diverse and representative range of irreversible dynamics, and the 6000 statistics adequately sample the key families from the literature.

What would settle it

An irreversible system (simulated or experimental) on which none of the 6000 statistics can reliably separate forward from time-reversed data, or the discovery of one statistic that indexes the form of irreversibility correctly for all 35 systems.

Figures

Figures reproduced from arXiv: 2511.15991 by Ben D. Fulcher, Teresa Dalle Nogare.

Figure 1
Figure 1. Figure 1: Schematic of our data-driven approach to identifying high-performing time-series statistics that can accurately index irreversibility from time-series data. (a) Time series generation: To include multiple and diverse sources of irreversibility, we simulated 5000-sample time series from a comprehensive library of 35 discrete-time and continuous-time processes with known reversibility properties. Each panel … view at source ↗
Figure 2
Figure 2. Figure 2: Identifying high-performing and interpretable time-series features for detecting irreversibility through large-scale empirical testing of thousands of features on 35 reversible and irreversible processes. (a) Distribution of cross-validated classification accuracy (of distinguishing reversible from irreversible processes) across 4668 features (excluding 1414 that are insensitive to reversibility, cf. Sec. … view at source ↗
Figure 3
Figure 3. Figure 3: Time-series features with time-symmetric constructions are invariant to time reversal, while time-asymmetric constructions can be powerful indices of time-reversibility. We illustrate this concept with respect to two families of time-series statistics: (a), (b): generalized autocorrelation functions; and (c), (d): the frequency of patterns of consecutive rises (‘up’: u) and falls (‘down’: d) in a symbolize… view at source ↗
Figure 4
Figure 4. Figure 4: All statistical time-series features have strengths and weaknesses at detecting irreversibility across different processes, demonstrating the need to tailor statistical summaries to the specific sources of irreversibility in a given process. (a) Box plot with scatter points showing the left-out accuracy of the 127 top-performing features for five representative irreversible processes: autoregressive with u… view at source ↗
read the original abstract

The dynamics of time-reversible systems are statistically indistinguishable when observed forward or backward in time. A rich literature of statistical methods to distinguish irreversible dynamics from the reversible dynamics of linear, Gaussian systems can provide insights into underlying mechanisms and aid modeling and statistical quantification of time-series data. But these existing time-reversibility metrics have been developed individually, forming a fragmented body of research that makes it challenging to identify the most effective approaches developed to date, and the most promising new directions for development. Here we address these issues by systematically evaluating over 6000 time-series summary statistics, derived from across the time-series analysis literature, on their ability to distinguish the time-irreversibility of data simulated from a diverse range of 35 systems. Our large-scale data-driven comparison highlights the effectiveness of several key families of statistics, including time-asymmetric forms of generalized autocorrelation functions, time-series symbolic sequences, and forecasting-related methods. All irreversible systems studied here could be accurately distinguished by a well-chosen time-series statistic, but no single statistic could accurately index the statistical form of irreversibility for all irreversible systems. This challenges the assumption that a given time-reversibility statistic will accurately capture time reversibility in general, and underscores the importance of tailoring statistical approaches to the time-reversal characteristics of a given system. Our results provide a unified understanding of the key algorithmic structures through which irreversibility can be effectively quantified from data, providing a foundation for connecting patterns in time series to the underlying mechanisms of the systems that generate them.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript conducts a large-scale empirical comparison of over 6000 time-series summary statistics, drawn from the broader literature, to assess their ability to detect time-irreversibility in simulated data from 35 dynamical systems. It reports that every irreversible system examined can be accurately distinguished by at least one well-chosen statistic, yet no single statistic succeeds across all systems, thereby challenging assumptions of universal time-reversibility metrics and advocating for system-specific tailoring.

Significance. If the empirical results are robust, the work supplies a valuable benchmark that unifies fragmented research on time-reversibility statistics and identifies effective algorithmic families (asymmetric autocorrelations, symbolic encodings, and forecasting-based methods). The scale of the comparison and the data-driven identification of structural patterns that capture irreversibility constitute clear strengths, offering a practical foundation for linking observed time-series features to underlying physical mechanisms.

major comments (2)
  1. Methods: The justification for selecting and classifying the 35 simulated systems is insufficient to establish that they span sufficiently heterogeneous irreversibility mechanisms (e.g., Hamiltonian, dissipative, multiplicative stochastic, and non-stationary classes) rather than parameter variations within a few families. This directly affects the load-bearing claim that no single statistic indexes irreversibility for all systems.
  2. Results / Abstract: The criterion used to declare that a system is 'accurately distinguished' is not defined (specific accuracy thresholds, ROC-AUC values, statistical tests, multiple-comparison corrections, or error estimation procedures). Without these details the central empirical finding lacks a verifiable quantitative basis.
minor comments (2)
  1. Abstract: The phrase 'diverse range of 35 systems' should be accompanied by a brief parenthetical classification of the system types to allow readers to assess coverage immediately.
  2. Notation: Consistent use of a single symbol for time-reversal (e.g., always T or always R) would improve readability across sections describing forward versus reversed series.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive comments on our manuscript. We address each of the major comments below and outline the revisions we will make to strengthen the paper.

read point-by-point responses

  1. Referee: Methods: The justification for selecting and classifying the 35 simulated systems is insufficient to establish that they span sufficiently heterogeneous irreversibility mechanisms (e.g., Hamiltonian, dissipative, multiplicative stochastic, and non-stationary classes) rather than parameter variations within a few families. This directly affects the load-bearing claim that no single statistic indexes irreversibility for all systems.

    Authors: We appreciate the referee pointing out the need for stronger justification of our system selection. The 35 systems were chosen to include representatives from distinct classes of irreversible dynamics, such as conservative Hamiltonian systems (e.g., nonlinear oscillators), dissipative systems (e.g., Lorenz attractor variants), multiplicative noise processes, and non-stationary time series. In the original manuscript, Section 2.2 describes the selection criteria and provides references for each system's known time-irreversibility properties. To further address this concern, we will add a supplementary table classifying each system by its primary mechanism and include a brief discussion of how parameter choices were made to avoid redundancy within families. We believe this will adequately support the diversity claim without altering the core results. revision: yes

  2. Referee: Results / Abstract: The criterion used to declare that a system is 'accurately distinguished' is not defined (specific accuracy thresholds, ROC-AUC values, statistical tests, multiple-comparison corrections, or error estimation procedures). Without these details the central empirical finding lacks a verifiable quantitative basis.

    Authors: We thank the referee for this observation. The manuscript employs a data-driven approach where a statistic is deemed effective if it allows reliable distinction between forward and time-reversed series using machine learning classifiers, with performance evaluated through cross-validation. To address the lack of explicit criteria, we will revise the Abstract and Results sections to explicitly define the accuracy thresholds, report ROC-AUC values, describe the statistical tests used (including any multiple-comparison corrections), and detail the error estimation procedures. This will ensure the central findings have a clear quantitative basis. revision: yes

Circularity Check

0 steps flagged

Empirical comparison of pre-existing statistics with no derivation circularity

full rationale

The paper performs a large-scale data-driven evaluation of over 6000 existing time-series statistics on simulated data from 35 systems to compare their effectiveness at detecting time-irreversibility. The central claims follow directly from these empirical outcomes rather than any mathematical derivation or prediction that reduces to fitted inputs or self-definitions. No load-bearing step relies on a self-citation chain that is itself unverified; the statistics are drawn from the broader literature and the results are falsifiable via the simulation benchmarks. Minor self-citation in the feature library is present but not circular for the reported findings.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the representativeness of the chosen systems and statistics; no free parameters or invented entities are described.

axioms (2)
  • domain assumption The 35 systems represent a diverse range of irreversible dynamics suitable for general conclusions.
    Stated in the abstract as the basis for the evaluation.
  • domain assumption The 6000 statistics cover the main families developed in the time-series literature.
    Implicit in the claim of a unified understanding from the comparison.

pith-pipeline@v0.9.0 · 5572 in / 1319 out tokens · 35169 ms · 2026-05-17T21:17:44.834602+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/ArrowOfTime.lean arrow_from_z echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    All irreversible systems studied here could be accurately distinguished by a well-chosen time-series statistic, but no single statistic could accurately index the statistical form of irreversibility for all irreversible systems.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    systematically evaluating over 6000 time-series summary statistics... on their ability to distinguish the time-irreversibility of data simulated from a diverse range of 35 systems

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supports
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Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Quo vadis, stochastic thermodynamics?

    cond-mat.stat-mech 2026-04 unverdicted novelty 1.0

    Stochastic thermodynamics is expanding to memory effects, active matter, geometric methods, and non-physical domains while the link between irreversibility and dissipation weakens at larger scales.

Reference graph

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