[Paper Review] Further Experimental Evidence of the Dead Matter Has Memory Conjecture in Capacitive Devices

Anis Allagui, Di Zhang+1 more|arXiv (Cornell University)|Jun 30, 2022

stochastic dynamics and bifurcation4 citations

TL;DR

This study provides experimental evidence that electric double-layer capacitors (EDLCs) exhibit a memory effect due to their non-ideal, fractional-order dynamics, where the statistical properties of prior voltage excitation—particularly noise variance—affect subsequent charge responses. Despite reaching identical voltage and charge endpoints, different charging waveforms with varying noise levels produce distinct discharge behaviors, confirming that EDLCs retain memory of their excitation history through fractional-order voltage-charge dynamics.

ABSTRACT

This study provides new sets of experimental results supporting Westerlund's conjecture that Dead Matter Has Memory. Memory effects in the dynamic response of electric double-layer capacitors (EDLCs) that integrate its prior history of stimulation and state have been experimentally observed and reported in a few recent studies. The different excitation signals used to quantify such effects in these studies aimed at charging a device to the same voltage value and the exact same accumulated charge level but in different manners. Having reached the same unique voltage-charge point, it was observed that different yet repeatable discharge patterns occur, proving the existence of memory. The aim of this work is to provide further experimental evidence of the inherent memory effect in EDLCs in response to time-varying stationary input excitations with different statistical properties. In particular, different sets of charging voltage waveforms composed of fixed dc values with superimposed uniformly-distributed random fluctuations of different amplitudes were created and used to charge the same EDLC device to a unique voltage-charge point. The duration of these signals was the same but with different values of variance around the mean value. We observed different time-charge responses depending on the extent of the noise level in these charging waveforms. This is interpreted and discussed in the context of inherent memory using fractional-order voltage-charge equations of non-ideal capacitors.

Motivation & Objective

• To provide further experimental validation of Westerlund's 'dead matter has memory' conjecture in non-ideal capacitors.
• To investigate how the statistical properties of time-varying voltage excitations—specifically variance of superimposed noise—affect the dynamic response of EDLCs.
• To demonstrate that EDLCs do not behave as ideal capacitors, as their charge response depends on the history of the input signal, not just the current state.
• To link the observed memory effect to fractional-order modeling, particularly through the influence of high-frequency components in the input on the memory trace term.

Proposed method

• Applied voltage waveforms composed of a fixed DC value with superimposed uniformly distributed random fluctuations of varying amplitudes (variances) to charge the same EDLC to a common voltage-charge point.
• Used discrete-time Fourier transforms (DTFT) to analyze the frequency content of the input signals, linking higher variance to stronger high-frequency components.
• Measured and compared time-charge and voltage-charge responses during charging and discharge phases under different noise levels.
• Calculated normalized cross-correlation between voltage and charge to quantify correlation strength and detect deviation from ideal capacitor behavior (Δq = C₁Δv).
• Numerically solved the fractional-order voltage-charge equation (Eq. 12) using estimated Cα = 0.660 F sec^(α−1) and α = 0.905 to simulate charge dynamics and validate experimental trends.
• Used the covariance-based correlation coefficient ρvq to quantify the degree of memory, with values ranging from -0.0491 to 0.2141 across different noise levels.

Experimental results

Research questions

• RQ1 Does the statistical variance of a time-varying voltage input influence the dynamic charge response of an EDLC, even when the final voltage and charge are identical?
• RQ2 To what extent does the memory effect in EDLCs manifest through deviations from the ideal capacitor constitutive relation Δq(t) = C₁Δv(t)?
• RQ3 How do the frequency content and harmonic components of the input signal correlate with the strength of the memory trace in fractional-order models?
• RQ4 Can the memory effect be quantitatively linked to the fractional-order parameter α and the CPE model parameters?

Key findings

• Different charging waveforms with the same final voltage and charge point but varying noise variance produced distinct discharge patterns, confirming the presence of memory in EDLCs.
• The normalized cross-correlation between voltage and charge decreased with increasing noise variance, indicating weaker correlation and deviation from ideal capacitor behavior.
• The correlation coefficient ρvq increased from -0.0491 (low variance) to 0.2141 (high variance), showing that higher noise levels lead to stronger memory effects.
• The DTFT analysis revealed that higher variance inputs contained stronger high-frequency components, which correlate with increased memory trace magnitude in fractional-order models.
• Numerical simulation of the fractional-order voltage-charge equation (Eq. 12) reproduced the experimental cross-correlation trends, validating the model's predictive power.
• The results confirm that EDLCs integrate past excitation history through a memory trace term dependent on α and input frequency content, supporting the 'dead matter has memory' conjecture.