gjphw@ihuxm.UUCP (03/24/84)
Hold on here!! In response to a question seeking clarification of the concepts around thermodynamics and probability, two well written articles were submitted (D. Mitchell and J. Stekas). I would like to make a request for consideration of an alternate view. I would like to suggest that there are two major schools of thought about the connection between probability (statistical mechanics) and thermodynamics. The view with the overwhelming number of adherents holds that dynamics (classical and quantum) is exact and thermodynamics is an approximation (in addition to being an idealization). Dynamics is the basis for statistical mechanics, and the usual source for the more fundamental understanding of the laws of thermodynamics comes from this study. A popular graduate level text on statistical mechanics (Huang) states that the second law of thermodynamics (entropy) is an approximation. The support of a bias toward dynamics is the outstanding success that can be realized using dynamical explanations for single particle interactions. A distinctly minority view, with support among some physical chemists, is that thermodynamics is exact and dynamics (or at least statistical mechanics) is an approximation. The major spokesman for this view is I. Prigogine in such texts as *From Being to Becoming*. In the experience of people who deal with large many body systems (N > 10^23), thermodynamics has never been observed to be violated and typical single particle dynamics is inadequate for the task of description. Prigogine (who is not a particularly lucid writer) argues that dynamics and statistical mechanics need modifications to bring them in agreement with thermodynamics (especially the second law). Non- equilibrium statistical mechanics might demonstrate the shortcomings of a dynamics only description, except for the fact that most expressions for these situations are too difficult to solve for the general case. You might be tempted to take your pick of these two schools with the proviso that the current consensus holds with the preeminence of dynamics. In the realm of large many body systems (e.g., a room full of air), the adequacy of single particle dynamics is not so clear. -- Patrick Wyant AT&T Bell Laboratories (Naperville, IL) *!ihuxm!gjphw
gwyn@brl-vgr.ARPA (Doug Gwyn ) (03/25/84)
But every time someone peeks at the microbehavior of a macro system such as a room full of air, he sees the micro-laws of physics being obeyed (no flames about the incompleteness of our knowledge of the laws, please). This is overwhelming confirmation for the consensus view of thermodynamics as statistical physics. One important point about physical understanding that was not emphasized in the schools I went to, but should have been, is that different points of view are more or less suitable for dealing with different situations. Trying to apply one single tool such as deterministic dynamics to all situations will get one in trouble (for lack of computational resources, if for no other reason).
alan@entropy.UUCP (Alan King) (03/27/84)
concerning a close look at a room full of air: Isn't the result of a close look at air or liquids the starting point for the development of Brownian motion? Once you begin examining things that small with that much energy, the paths are not even differentiable! Thus it is hard to see the justification for the comment that dynamical laws explain motion in the microscale. To put it another way: there is no interval of time of positive length during which an individual molecule of air travels along a "classical" trajectory. The path is known only in a statistical sense even for individual particles. Of course the dynamical laws must be obeyed -- but they cannot be used to explain the motion of individual particles in a swarm of air. It was the attempt to explain this motion that led Einstein to develop his explanation of Brownian motion. alan king dept of mathematcs university of washington
mam@charm.UUCP (Matthew Marcus) (03/31/84)
Entropy!alan claims that the paths of molecules in gases aren't even differentiable, much less explainable by micro-dynamic. Sorry, that's rubbish! True, if you look *at a certain length scale*, the paths appear pretty noisy, but they are quite continuous and differentiable when examined with resolution below the mean free path. For a hard-sphere gas, the path is non-differentiable at the collision points, but there's no such thing as a hard-sphere gas, except inside a computer. That reminds me, lots pf people use molecular dynamics (integrating micro equations of motion on a computer) to explain macro properties of gases, liquids, and solids. {BTL}!charm!mam
gwyn@brl-vgr.ARPA (Doug Gwyn ) (03/31/84)
Sorry to poke a hole in your argument but molecular motion in a gas is not "fractal". Look up "mean free path" and you will see what I mean.
mwg@allegra.UUCP (Mark Garrett) (04/10/84)
No; all the air molecles in a room could not, by themselves, move to one side. Statistical mechanics inherently is not accurate enough (nor has it been verified experimentally accurately enough) to predict correctly such improbable events as all air molecules *by themselves* drifting to one side of the room. Although the examples--(1) a growing crystal, or (2) a gravitational dust cloud condensing into planets, of (3) chemical processes that formed life--represent increases in entropy and at the same time increases in order, nevertheless these examples all occur at the expense of even more disorder (simultaneouus irreversible processes) in the universe: (1) heat flow from hot to cold bodies, (2) emmitted noise and other radiation, as well as conversion of (ordered) potential gravitational energy into (disordered) heat, and (3) consumption of nuclear fuel on the sun. Besides, statistical mechanics rests upon the assmpution of the truth of the ergodic (or quasi-ergodic) hypothesis--i.e., the hypothesis that the universe comes back to its initial state (or as closely so as can be specified) or to any other given state (or closely so) if only you wait long enough. This hypothesis is obviously false. After you die, the universe will never, repeat *never*, comeback to its present state (or closely so)--i.e., with all calendars on the earth displaying a year "1984" (or "1914") and with you alive (except that you are insane). -D.I. Caplan Bell Labs, Murray Hill {this opinion represents neither that of this coropration or even the owner of this account}
steve@Brl-Bmd.ARPA (04/15/84)
From: Stephen Wolff <steve@Brl-Bmd.ARPA> >> From: hplabs!tektronix!uw-beaver!uw-june!entropy!alan@Ucb-Vax.ARPA >> >> Isn't the result of a close look at air or liquids the >> starting point for the development of Brownian motion? >> Once you begin examining things that small with that much >> energy, the paths are not even differentiable! Oh, baloney! These aren't small particles you're talking about - they're m o l e c u l e s ! The paths are for ALL intents and purposes classical. The ABSTRACTION called `Brownian motion' or the `Wiener process' is just that - a very pretty passage to a `conceptual limit' of molecular motion. It's the ABSTRACTION that has all the lovely properties - almost everywhere non-differentiabilty, linearly growing variance, independent increments, the lot - but the REAL process ain't so accommodating.