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The physiology is that air is trapped in the stomach. The stomach doesn't need or want air, so it tries to expel it as a burp. It's a reflex. But the air is blocked by the esophagus, which doesn't want stomach contents coming up unless unavoidably necessary (projectile vomiting, retching).

So by taking a deep breath and holding, the reflex is interrupted and on the expulsion of a large volume of breath, the whole trunk of the body relaxes and the trapped air can escape.

What I do is related. I arch my head up, and purposefully relax my esophagus to release the trapped air. Voluntary nervous system over involuntary. I kind of "burp myself". It is that simple, as is yours though yours is more of a trick subverting the involuntary nerves. You can do it in a dry desert with no water, while standing in a crowd, no fuss.