Final answer:
While the Poincaré recurrence theorem theoretically allows systems to return to their original state after a long time, in reality, for macroscopic systems like a container of sand, the probability is incredibly low due to high particle number and entropy's role in favoring disordered states.
Step-by-step explanation:
The question seems to be rooted in the concept of entropy and how it relates to systems returning to their original state. The Poincaré recurrence theorem suggests that certain systems will, after a sufficiently long time, return to a state very close to the initial state. However, in practical terms, the probabilities of such an event in a macroscopic system (like a sand shaker) are astronomically low due to the incredibly high number of particles and their interactions, which practically nullify the chance of reverting to the initial arrangement. This is in contrast with the more likely scenario where entropy increases, resulting in a more disordered state rather than an ordered one, as observed in everyday experiences like a messy bedroom becoming messier.
Moreover, from a microscopic standpoint, while the laws of physics don't prohibit microscopic particles from reverting to their original states (due to time-symmetric Newtonian mechanics), the cumulative effect over a macroscopic number of particles (greater than 1023) such as grains of sand results in a phenomena where any 'memory' of the initial conditions is effectively erased.
The concept of entropy is key here. It is entropy that makes more ordered states less likely to spontaneously emerge. This can be visualized by considering how unlikely it is for a broken mug's pieces to spontaneously assemble back into a whole mug, as mentioned in the example about ceramic pieces on a floor.