Boltzmann's View of the Second Law as a Law of Disorder

The active macroscopic nature of the second law posed a direct challenge to the "dead" mechanical world view which Boltzmann tried to meet in the latter part of the last century by reducing the second law to a law of probability following from the random collisions of mechanical particles (efficient cause (see Swenson (1990)). Following the lead of Maxwell who had modeled gas molecules as colliding billiard balls, Boltzmann argued that the second law was simply a consequence of the fact that since with each collision nonequilibrium distributions would become increasingly disordered leading to a final state of macroscopic uniformity and microscopic disorder. Because there are so many more possible disordered states than ordered ones, he concluded, a system will almost always be found either in the state of maximum disorder or moving towards it.
As a consequence, a dynamically ordered state, one with molecules moving "at the same speed and in the same direction," Boltzmann (1974/1886, p. 20) asserted, is thus "the most improbable case infinitely improbable configuration of energy." Because this idea works for certain near equilibrium systems such as gases in boxes, and because science until recently was dominated by near equilibrium thinking, Boltzmann's attempted reduction of the second law to a law of disorder became widely accepted as the second law rather than simply an hypothesis about the second law, and one that we now know fails. It became the apparent justification from physics for solidifying Cartesian incommensurability and establishing the view of the two incommensurable rivers-the "river" of biology, psychology, and culture, or the epistemic dimension of the world characterized by intentional dynamics and flowing up to increasingly higher states of order, versus the "river" of physics flowing down to disorder. Such a view is entirely inimical to a science of ecological relations, since, as noted above, it is precisely through the interface of these two rivers that these relations occur, and if the interface is incommensurable then the relations are effectively prohibited, or at best, incomprehensible.

Two time slices from the Bénard experiment. When the gradient of the potential (the "force") between source (the heated surface below) and the sink (the cooler air at the top) is below a critical threshold (left) the flow of heat is produced by the random collision of the molecules (conduction), and the system is in the disordered or "Boltzmann regime", and the surface of the system is smooth, homogeneous, and symmetrical. When the force is above the critical threshold (right), however, the symmetry of the system is broken and autocatakinetic order spontaneously arises as random microscopic fluctuations are amplified to macroscopic levels and "Benard cells" fill the container as hundreds of millions of molecules begin moving together (for more detailed discussion see e.g., Swenson, 1989a,b, c, 1992, 1997a). (From Swenson, 1989c. Copyright 1989 Pergamon Press. Used by permission).

entropy main

classical view of entropy