We present a predictive Geometric Stress Index (pGSI) and its relation to behavioural Entropy ([Formula: see text]). [Formula: see text] is a measure of the complexity of an organism's reactivity to stressors yielding patterns based on different behavioural and physiological variables selected as Surrogate Markers of Stress (SMS). We present a relationship between pGSI and [Formula: see text] in terms of a power law model. This nonlinear relationship describes congruences in complexity derived from analyses of observable and measurable SMS based patterns interpreted as stress. The adjective geometric refers to subdivision(s) of the domain derived from two SMS (heart rate variability and steps frequency) with respect to a positive/negative binary perceptron based on a third SMS (blood oxygenation). The presented power law allows for both quantitative and qualitative evaluations of the consequences of stress measured by pGSI. In particular, we show that elevated stress levels in terms of pGSI leads to a decrease of the [Formula: see text] of the blood oxygenation, measured by peripheral blood oxygenation SpO2 as a model of SMS.