A journalist I am following on twitter just posted the question in the title of this post. I felt bound to try and give an answer with as simple concepts as I found meaningful. So, what makes a unstable particle unstable ?

One answer is this: a particle is unstable if there is a way, not forbidden by any physical law, to convert its rest-mass into other forms of energy. One may understand this by thinking at entropy: any system left free to evolve will do so in the direction of maximum entropy. So since a single particle state is a very low-entropy system, while the decay products of its disintegration have a multitude of possible configurations and a higher entropy, the system will naturally evolve in that direction.
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