Do you seriously want to incentivize productive behavior during people's work breaks? Because that doesn't sound to me like something you want to incentivize (risk of burnout etc.).

No, I'm taking a quick break from my "work" to help a valued colleague solve a problem informally in a way that actually adds more value to the organisation than if I had been sat at my desk. I enjoy the human interaction, its good for my sense of wellbeing. My colleague has his stress levels reduced. We learn a bit about each other's jobs in those 15 minutes and a product is delivered a week earlier than it would otherwise have been.