The physiological sigh is a double inhale through the nose, a short second inhale on top of the first, followed by one long, slow exhale through the mouth. It is the same pattern your body performs naturally when you are crying or catching your breath, borrowed and used on purpose.
In the same Stanford-led randomised controlled trial mentioned on the Box Breathing page, cyclic sighing was tested against box breathing, four-count breathing, and a period of mindfulness meditation, with 111 participants practising for five minutes a day over a month. Cyclic sighing produced the largest improvement in mood and the biggest drop in resting breathing rate of the four groups.
It works well as a fast reset in the middle of something: a wave of frustration at your desk, the moment before you walk back into a room. It will not resolve an ongoing anxiety disorder on its own, and it is not a substitute for treatment if anxiety is a regular part of your life. For a stressor you can see coming, where you have a few minutes rather than a few seconds, box breathing is often the better fit.