How much economic activity happens?

Some things tend to increase the amount of paid work done, such as the wish to make money, while other things tend to decrease it, such as leisure preference. Total economic output balances the two. Can more complicated equations be derived showing how much economic activity happens at any time?

I think a little econophysics might help to answer the question. Econophysics is the application of physical science to economics, and has some attention in the economics literature. Mainstream economics has always borrowed from physics and applied mathematics, but econophysics tries to make very close analogies.

I am thinking about minimisation of energy in a particle's flight when thrown upwards. A particle minimises the amount of energy it takes to move, so that the integral I(kinetic energy - potential energy) is minimised at all times. The principle is equivalent to saying that the particle moves under the influences of forces acting on it (kinetic energy upwards, potential energy downwards), and only on them. The analogy with economic activity is clear - an economy grows (respectively, contracts) only if the effect of the forces on it is positive (respectively, negative). I am not presently smart enough at physics to determine how energy, force, and the minimisation equation are exactly related, and the economics version of the integral minimisation may not be in precisely the same form.

If the economics integral could be established, there could be some snazzy toys waiting. The integral minimisation in physics gives rise to such helpful relations as the conservation of energy, and similar expressions may be available in economics. Answering how much activity occurs at any point in time would be a great result.