4. The arrow of time

‘The arrow of time’ discusses where the arrow of time comes from. The fundamental laws of motion do not distinguish past and future. And yet the everyday world is full of manifestly asymmetric processes. This chapter discusses the apparent mismatch between the fundamental laws of nature and the manifest asymmetry of the everyday world. The temporal asymmetry is made precise by the second law of thermodynamics and the tension between the second law and the fundamental laws is addressed by the development of statistical mechanics.

A Review of Functions of Speculative Thinking

Speculative thinking refers to thinking about past or future possibilities; it includes counterfactual thinking, prefactual thinking, and other types. In this narrative review, we discuss the traditional function of speculative thinking in improving future performance (i.e., the preparatory function). We also explore several non-preparatory functions of speculative thinking that have not been widely covered, namely the functions of conveying information and of supporting lying. In addition, we address temporal asymmetry; one perspective focuses on psychological distance in speculative thinking about the past and future, while another focuses on temporal asymmetry and reality/hypothetical differences in the preparatory function of speculative thinking. Overall, this review suggests that a broader functional theory is needed to address non-preparatory functions and the traditional preparatory function. Such a theory should cover all speculative thinking about the past and future rather than simply counterfactual thinking.

Temporal irreversibility of neural dynamics as a signature of consciousness

Even though the fundamental laws of physics are the same when the direction of time is inverted, dissipative systems evolve in the preferred temporal direction indicated by the thermodynamic arrow of time. The fundamental nature of this temporal asymmetry led us to hypothesize its presence in the neural activity evoked by conscious perception of the physical world, and thus its covariance with the level of conscious awareness. Inspired by recent developments in stochastic thermodynamics, we implemented a data-driven and model-free deep learning framework to decode the temporal inversion of electrocorticography signals acquired from non-human primates. Brain activity time series recorded during conscious wakefulness could be distinguished from their inverted counterparts with high accuracy, both using frequency and phase information. However, classification accuracy was reduced for data acquired during deep sleep and under ketamine-induced anesthesia; moreover, the predictions obtained from multiple independent neural networks were less consistent for sleep and anesthesia than for conscious wakefulness. Finally, the analysis of feature importance scores highlighted transitions between slow (≈20 Hz) and fast frequencies (> 40 Hz) as the main contributors to the temporal asymmetry observed during conscious wakefulness. Our results show that a preferred temporal direction is simultaneously manifest in the neural activity evoked by conscious mentation and in the phenomenology of the passage of time, establishing common ground to tackle the relationship between brain and subjective experience.

Waveform Amplitude and Temporal Symmetric/Asymmetric Characteristics of Phoneme and Syllable Segments in the W-1 Spondaic Words Recorded by Four Speakers

Background The amplitude and temporal asymmetry of the speech waveform are mostly associated with voiced speech utterances and are obvious in recent graphic depictions in the literature. The asymmetries are attributed to the presence and interactions of the major formants characteristic of voicing with possible contributions from the unidirectional air flow that accompanies speaking. Purpose This study investigated the amplitude symmetry/asymmetry characteristics (polarity) of speech waveforms that to our knowledge have not been quantified. Study Sample Thirty-six spondaic words spoken by two male speakers and two female speakers were selected because they were multisyllabic words providing a reasonable sampling of speech sounds and four recordings were available that were not related to the topic under study. Research Design Collectively, the words were segmented into phonemes (vowels [130], diphthongs [77], voiced consonants [258], voiceless consonants [219]), syllables (82), and blends (6). For each segment the following were analyzed separately for the positive and negative datum points: peak amplitude, the percent of the total segment datum points, the root-mean-square (rms) amplitude, and the crest factor. Data Collection and Analyses The digitized words (44,100 samples/s; 16-bit) were parsed into 144 files (36 words × 4 speakers), edited, transcribed to numeric values (±1), and stored in a spread sheet in which all analyses were performed with in-house routines. Overall approximately 85% of each waveform was analyzed, which excluded portions of silent intervals, transitions, and diminished waveform endings. Results The vowel, diphthong, and syllable segments had durations (180–220 ms) that were about twice as long as the consonant durations (∼90 ms) and peak and rms amplitudes that were 6 to 12 dB higher than the consonant peak and rms amplitudes. Vowel, diphthong, and syllable segments had 10% more positive datum points (55%) than negative points (45%), which suggested temporal asymmetries within the segments. With voiced consonants, the distribution of positive and negative datum points dropped to 52 and 48% and essentially was equal with the voiceless consonants (50.3 and 49.6%). The mean rms amplitudes of the negative datum points were higher than the rms amplitudes for the positive points by 2 dB (vowels, diphthongs, and syllables), 1 dB (voiced consonants), and 0.1 dB (voiceless consonants). The 144 waveforms and segmentations are illustrated in the Supplementary Material along with the tabularized positive and negative segment characteristics. Conclusions The temporal and amplitude waveform asymmetries were by far most notable in segments that had a voicing component, which included the voiced consonants. These asymmetries were characterized by larger envelopes and more energy in the negative side of the waveform segment than in the positive side. Interestingly, these segments had more positive datum points than negative points, which indicated temporal asymmetry. All aspects of the voiceless consonants were equally divided between the positive and negative domains. There were female/male differences but with these limited samples such differences should not be generalized beyond the speakers in this study. The influence of the temporal and amplitude asymmetries on monaural word-recognition performance is thought to be negligible.

Streamflow indices to identify catchment drivers of hydrograph

Streamflow indices are flow descriptors that quantify the streamflow dynamics, which are usually determined for a specific basin and are distinct from other basin features. The flow descriptors are appropriate for large-scale and comparative hydrology studies, independent of statistical assumptions and can distinguish signals that indicate basin behavior over time. In this paper, the characteristic features of the hydrograph's temporal asymmetry due to its different underlying hydrologic processes are primarily highlighted. Streamflow indices linked to each limb of the hydrograph within the time-irreversibility paradigm are distinguished with respect to its processes driving the rising and falling limbs. Various streamflow indices relating the rising and falling limbs, and the catchment attributes such as climate, topography, vegetation, geology and soil are then correlated. Finally, the key attributes governing rising and falling limbs are identified. The novelty of the work is on differentiating hydrographs by their time irreversibility property and offering an alternative way to recognize primary drivers of streamflow hydrographs. A set of streamflow indices at the catchment scale for 671 basins in the Contiguous United States (CONUS) is presented here. These streamflow indices complement the catchment attributes provided earlier (Addor et al., 2017) for the CAMELS data set. A series of spatial maps describing the streamflow indices and their regional variability over the CONUS is illustrated in this study.

Evaluation of Re-analyses Over China based on the Temporal Asymmetry of Daily Temperature Variability

As an intrinsic feature of daily surface air temperature (SAT) variability found in station measurements, temporal asymmetry (TA) can be taken as an evaluation metric to access the quality of SAT re-analysis product. In this study, TA calculated from four SAT variables, i.e. daily mean SAT (Tmean), daily maximum SAT (Tmax), daily minimum SAT (Tmin) and diurnal temperature range (TDTR=Tmax-Tmin), is applied to evaluate synoptic-scale performance of four reanalysis products (NCEP-2, JRA-55, ERA-I and ERA-5) over China. The results show that four re-analyses overall overestimate the TA of daily Tmax and Tmin variability over China, but with a comparatively consistent estimated TA for Tmean. Moreover, the TA of Tmean variability for these four re-analyses shares high spatial consistency with those from the observation. However, four re-analyses own the similar region-dependent spatial patterns of overestimated TA for Tmax and Tmin variability, especially for Tmax. Since high TA is an indicator for strong nonlinear feature, only Tmean reanalysis is the most suitable to explore synoptic-scale extreme events, such as heat waves and cold waves, which are highly related to the strong nonlinear processes.

Effect of robotic-assisted gait training on objective biomechanical measures of gait in persons post-stroke: a systematic review and meta-analysis

Background Robotic-Assisted Gait Training (RAGT) may enable high-intensive and task-specific gait training post-stroke. The effect of RAGT on gait movement patterns has however not been comprehensively reviewed. The purpose of this review was to summarize the evidence for potentially superior effects of RAGT on biomechanical measures of gait post-stroke when compared with non-robotic gait training alone. Methods Nine databases were searched using database-specific search terms from their inception until January 2021. We included randomized controlled trials investigating the effects of RAGT (e.g., using exoskeletons or end-effectors) on spatiotemporal, kinematic and kinetic parameters among adults suffering from any stage of stroke. Screening, data extraction and judgement of risk of bias (using the Cochrane Risk of bias 2 tool) were performed by 2–3 independent reviewers. The Grading of Recommendations Assessment Development and Evaluation (GRADE) criteria were used to evaluate the certainty of evidence for the biomechanical gait measures of interest. Results Thirteen studies including a total of 412 individuals (mean age: 52–69 years; 264 males) met eligibility criteria and were included. RAGT was employed either as monotherapy or in combination with other therapies in a subacute or chronic phase post-stroke. The included studies showed a high risk of bias (n = 6), some concerns (n = 6) or a low risk of bias (n = 1). Meta-analyses using a random-effects model for gait speed, cadence, step length (non-affected side) and spatial asymmetry revealed no significant differences between the RAGT and comparator groups, while stride length (mean difference [MD] 2.86 cm), step length (affected side; MD 2.67 cm) and temporal asymmetry calculated in ratio-values (MD 0.09) improved slightly more in the RAGT groups. There were serious weaknesses with almost all GRADE domains (risk of bias, consistency, directness, or precision of the findings) for the included outcome measures (spatiotemporal and kinematic gait parameters). Kinetic parameters were not reported at all. Conclusion There were few relevant studies and the review synthesis revealed a very low certainty in current evidence for employing RAGT to improve gait biomechanics post-stroke. Further high-quality, robust clinical trials on RAGT that complement clinical data with biomechanical data are thus warranted to disentangle the potential effects of such interventions on gait biomechanics post-stroke.

Variations in stability revealed by temporal asymmetries in contraction of phase space flow

Empirical diagnosis of stability has received considerable attention, often focused on variance metrics for early warning signals of abrupt system change or delicate techniques measuring Lyapunov spectra. The theoretical foundation for the popular early warning signal approach has been limited to relatively simple system changes such as bifurcating fixed points where variability is extrinsic to the steady state. We offer a novel measurement of stability that applies in wide ranging systems that contain variability in both internal steady state dynamics and in response to external perturbations. Utilizing connections between stability, dissipation, and phase space flow, we show that stability correlates with temporal asymmetry in a measure of phase space flow contraction. Our method is general as it reveals stability variation independent of assumptions about the nature of system variability or attractor shape. After showing efficacy in a variety of model systems, we apply our technique for measuring stability to monthly returns of the S&P 500 index in the time periods surrounding the global stock market crash of October 1987. Market stability is shown to be higher in the several years preceding and subsequent to the 1987 market crash. We anticipate our technique will have wide applicability in climate, ecological, financial, and social systems where stability is a pressing concern.

Simple stochastic model for geomagnetic excursions and reversals reproduces the temporal asymmetry of the axial dipole moment

We present a simple model for the axial dipole moment (ADM) of the geomagnetic field based on a stochastic differential equation for two coupled particles in a biquadratic potential, subjected to Gaussian random perturbations. This model generates aperiodic reversals and excursions separated by stable polarity periods. The model reproduces the temporal asymmetry of geomagnetic reversals, with slower decaying rates before the reversal and faster growing rates after it. This temporal asymmetry is possible because our model is out of equilibrium. The existence of a thermal imbalance between the two particles sets a preferential sense for the energy flux and renders the process irreversible.