How to interpret the passivity criteria equation?

In Passivity-Based Control and Estimation in Networked Robotics (among others), a passive system is defined as one that:

$$\int_0^t y^T(t)u(t) dt \geq -\beta$$

for output $$y$$ and input $$u$$.

I have never understood how this describes a system where

the total internal energy stored in the system is bounded above by the energy externally supplied to the system

This comes down to $$y$$ and $$u$$ being under defined.

• One way to interpret it, is since we are discussing energy, that $$u$$ and $$y$$ have units that result in their product being a measure of energy? And implicitly that the integral defines some energy reservoir or dissipation?

• Alternatively, the only way that the above is violated, is if $$y$$ is negatively proportional to $$u$$? But what does that mean mechanically? That the robot is compliant?

How should I imagine $$y$$ and $$u$$ in order to make sense of the passivity criteria above?