Posted Nov 21, 2012 9:08 UTC (Wed) by man_ls
In reply to: Good piece
Parent article: LCE: Don't play dice with random numbers
The second law of thermodynamics is not a consequence of reservoirs; they are just an artifact introduced to model and simplify the outside world, since the second law works just as well without them.
It goes a bit further than that: perfect information about any system is unattainable in classical mechanics. Infinite bits would be needed just to keep the state of a single particle, let alone 10^23 of them, let alone placing them in a non-linear system, let alone computing anything beyond a perfect gas. No matter how paranoid you are, modeling a real world gas particle by particle is not feasible.
In fact, a modern information-theoretic formulation of the second law would say that "to extract one bit of information from a system you have to reduce its entropy in one bit", which explains why perfect information about systems cannot be achieved. Many people believe that only quantum mechanics say that "observation modifies the system being observed", but it is not so.
To find a formulation to which both of us can agree, we might say that "classical mechanics has an element of randomness unless we have perfect information about a system; perfect information cannot be achieved; therefore classical mechanics is random in nature".
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