> In fact the second law of thermodynamics (which incidentally was
> postulated before the first) ensures that knowledge about the system will
> degrade in time, so even if perfect information is held at the start, any
> system will quickly degrade into random patterns. It is not an artifact of
> our limitations, but an essential principle of nature. We will never be
> able to predict the minute variations in thermal noise, no matter how much
> we know about the system.
Thermodynamics implies that a reservoir is involved in the modelling of a physical process, and that this reservoir is only treated effectively (any degrading system implies such a reservoir; otherwise, there would be nothing it could degrade into). If all parts of the system were treated with the dynamical laws of classical mechanics, it would not be necessary to fall back to a thermodynamic approximation. There would also be no reservoir.
So using a reservoir to model a physical system amounts to a lack of knowledge, which in turn causes the perceived randomness.
> As for macroscopic randomness, the humble three-body problem in
> gravitation generates a chaotic system using only classical equations:
> minor deviations cause major, unpredictable changes in the system.
A chaotic system is by its very definition a deterministic system. Initially close states may diverge arbitrarily far by temporal propagation (loosely spearking; things become more involved when the associated phase space volume can shrink), but the individual trajectories are still governed by deterministic dynamics.
They are very well predictable. If the initial conditions could be determined with infinite accuracy -- which, in the framework of classical mechanics, is theoretically possible -- there is no randomness involved.
But admittedly, these considerations are for the /really/ paranoid. Solving coupled dynamical equations of 10**23 or so particles certainly presents a /tiny/ practical problem ;)