Chaos in oscillatory heat evolution accompanying the sorption of hydrogen and deuterium in palladium

TL;DR

This paper presents a new method to distinguish deterministic chaos from randomness in heat oscillations during hydrogen and deuterium sorption in palladium, demonstrating that observed aperiodic oscillations are likely chaotic.

Contribution

A novel chaos detection test based on a theorem relating function derivatives and integrals was developed and applied to calorimetric data, confirming chaos in palladium sorption oscillations.

Findings

Oscillations in heat evolution are likely deterministic chaos.

Test results cluster near zero for deterministic datasets.

Experimental data show results close to zero, indicating chaos.

Abstract

Aperiodic oscillations in the sorption of H2 or D2 in metallic Pd powder have been observed, and a novel method to confirm their deterministic rather than random character has been devised. A theorem relating the square of a function, with the derivative and integral with variable upper limit of the same function has been proved and proposed to be used as a base for a chaos-vs-random test. Both the experimental and the computed time series may be tested to detect determinism. The result is a single number within the interval [0,2]. The test is designed in such a way that its result is close to zero for the datasets that are deterministic and smooth, and close to 2 for the datasets that are non deterministic (random) or non smooth (discrete). A large variety of the test results has been obtained for the calorimetric time series recorded in thermokinetic oscillations, periodic and quasiperiodic, accompanying the sorption of H2 or D2 with Pd as well as for several non oscillatory calorimetric curves recorded in this reaction. These experimental datasets, all coming form presumably deterministic processes, yielded the results clustering around 0.001. On the other hand, certain databases that were presumably random or non smooth yielded the test results from 0.7 to 1.9. Against these benchmarks, the examined, experimental, aperiodic oscillations gave the test results between 0.004 and 0.01, which appear to be much closer to the deterministic behavior than to randomness. Consequently, it has been concluded that the examined cases of aperiodic oscillations in the heat evolution accompanying the sorption of H2 or D2 in palladium may represent an occurrence of mathematical chaos in the behavior of this system. Further applicability and limitations of the test have also been discussed, including its intrinsic inability to detect determinism in discrete time series.