Lynn (2014) published a study in Evolutionary Psychology examining hearth and campfire influences on arterial blood pressure. Fire with sound produced consistent blood pressure decreases, with longer exposure producing greater effects. The calming response is attributed to deep evolutionary associations with safety, warmth, and social gathering around fire.
The stochastic timing of crackle events follows approximately a Poisson distribution (random, memoryless timing). This prevents auditory habituation, meaning the brain does not tune out the sound as quickly as it would with steady-state noise. Each crackle is a brief broadband impulse (2-8 kHz) that provides micro-variation without being startling.
Note: The Lynn study used visual and audio together. The audio-only effect is not isolated in the literature. No ADHD-specific study exists for fireplace sounds.