On Tue, Sep 07, 2010 at 10:22:57PM -0400, Jerry Leichter wrote: > But there isn't actually such a thing as classical thermodynamical > randomness! Classical physics is fully deterministic. Thermodynamics uses > a probabilistic model as a way to deal with situations where the necessary > information is just too difficult to gather. Classically, you could in > principle measure the positions and momenta of all the atoms in a cubic > liter of air, and then produce completely detailed analyses of the future > behavior of the system. There would be no random component at all. In > practice, even classically, you can't hope to get even a fraction of the > necessary information - so you instead look at aggregate properties and, > voila, thermodynamics. There's no randomness assumption - much less an > unpredictability assumption - for the micro-level quantities. What you > need is some uniformity assumptions. If I had access to the full micro > details of that liter of air, your calculations of the macro quantities > would be completely undisturbed.
This glosses over the *fundamental* complexity of non-linear classical dynamics. It is a leap to claim that the underlying determinism of a classical dynamical system leads one to conclude that it is even in principle "predictable", in the presence of chaos. We should not short-change classical "chaos" which is an emergent property of complex deterministic systems. http://www-chaos.umd.edu/research.html ... Riddled Basins The notion of determinism in classical dynamics has eroded since Poincar??'s work led to recognition that dynamical systems can exhibit chaos: small perturbations grow exponentially fast. Hence, physically ubiquitous measurement errors, noise, and computer roundoff strongly limit the time over which, given an initial condition, one can predict the detailed state of a chaotic system. Practically speaking, such systems are nondeterministic. Notwithstanding the quantitative uncertainty caused by perturbations, the system state is confined in phase space (on an "attractor") so at least its qualitative behavior is predictable. Another challenge to determinism arises when systems have competing attractors. With a boundary (possibly geometrically convoluted ) between sets of initial conditions tending to distinct attractors ("basins of attraction"), perturbations make it difficult to determine the fate of initial conditions near the boundary. Recently, mathematical mappings were found that are still worse: an attractor's entire basin is riddled with holes on arbitrarily fine scales. Here, perturbations globally render even qualitative outcomes uncertain; experiments lose reproducibility. J.C. Sommerer and E. Ott, "A Qualitatively Nondeterministic Physical System", Nature, 365, 135 (1993). -- Viktor. --------------------------------------------------------------------- The Cryptography Mailing List Unsubscribe by sending "unsubscribe cryptography" to majord...@metzdowd.com