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Aperiodic oscillations in the sorption of H2 or D2 in metallic Pd powder havebeen observed, and a novel method to confirm their deterministic rather thanrandom character has been devised. A theorem relating the square of a function,with the derivative and integral with variable upper limit of the same functionhas 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 detectdeterminism. The result is a single number within the interval [0,2]. The testis designed in such a way that its result is close to zero for the datasetsthat are deterministic and smooth, and close to 2 for the datasets that are nondeterministic (random) or non smooth (discrete). A large variety of the testresults has been obtained for the calorimetric time series recorded inthermokinetic oscillations, periodic and quasiperiodic, accompanying thesorption of H2 or D2 with Pd as well as for several non oscillatorycalorimetric curves recorded in this reaction. These experimental datasets, allcoming form presumably deterministic processes, yielded the results clusteringaround 0.001. On the other hand, certain databases that were presumably randomor non smooth yielded the test results from 0.7 to 1.9. Against thesebenchmarks, the examined, experimental, aperiodic oscillations gave the testresults between 0.004 and 0.01, which appear to be much closer to thedeterministic behavior than to randomness. Consequently, it has been concludedthat the examined cases of aperiodic oscillations in the heat evolutionaccompanying the sorption of H2 or D2 in palladium may represent an occurrenceof mathematical chaos in the behavior of this system. Further applicability andlimitations of the test have also been discussed, including its intrinsicinability to detect determinism in discrete time series.

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