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(See for example David Chandler, Introduction to Modern Statistical Mechanics, Chap. In contrast, for a real gas subject to no external forces, an atom is equally likely to occupy any position within its container, but pairs of atoms are correlated. But the speed of the atom is very much not “equally likely to have any value”: indeed, the probability of the atom having speed between v and v + dv is given by the Maxwell-Boltzmann distribution 2 π ( m k B T ) 3 v 2 e − m v 2 / 2 k B T d v. The velocity of the atom is equally likely to point in any direction.

Given the vagueness of the word “disorder,” we must ask the exact meaning of the phrase “a gas at equilibrium is disordered.” First consider an ideal gas subject to no external forces: An atom is equally likely to occupy any position within its container, and pairs of atoms are uncorrelated. Brush, The Kind of Motion We Call Heat ( North-Holland, Amsterdam, 1976). Ray Nelson Faulkner, Art Today: An Introduction to the Fine and Functional Arts ( Holt, Rinehart and Winston, New York, 1956), p. Parker Tyler, “ Jackson Pollock: The infinite labyrinth,” Magazine of Art 43 (3), 92– 93 ( March 1950). Micolich, and David Jonas, “ Fractal analysis of Pollock’s drip paintings,” Nat. See, for example, Ihsan Barin, Thermochemical Data of Pure Substances ( VCH Publishers, Weinheim, Germany, 1995). See Table II in Daphne Lofquist, Terry Lugaila, Martin O’Connell, and Sarah Feliz, “ Households and Families: 2010,” U.S. In the 2010 census, the average American family had 3.14 members-π to three significant digits-despite the fact that no family whatsoever had 3.14 members. A more extreme example comes from family size.

2 would be absolutely typical for a window containing one-millionth of the total sites. This conclusion cannot be avoided by invoking “the law of large numbers” or “the thermodynamic limit.” For if we had a million times more squares scattered on a million times more sites, then the configurations in Fig. Freeman and Company, San Francisco, 1963) p. Taylor and John Archibald Wheeler, Spacetime Physics, 1st ed. A wrong guess brings the refreshment of surprise.” Edwin F. Courage: no one else needs to know what the guess is. Schroeder, “ A different approach to introducing statistical mechanics,” Am. Silverstein, “ The real reason why oil and water don’t mix,” J. By “uniform” I mean “uniform on a macroscopic scale.” All phases of all materials are of course granular on the atomic scale.