Elsevier has just published Granville Sewell’s “A Second Look at the Second Law” (Applied Mathematics Letters, June 2011):
ABSTRACT: It is commonly argued that the spectacular increase in order which has occurred on Earth does not violate the second law of thermodynamics because the Earth is an open system, and anything can happen in an open system as long as the entropy increases outside the system compensate the entropy decreases inside the system. However, if we define ‘‘X-entropy’’ to be the entropy associated with any diffusing component X (for example, X might be heat), and, since entropy measures disorder, ‘‘X-order’’ to be the negative of X-entropy, a closer look at the equations for entropy change shows that they not only say that the X-order cannot increase in a closed system, but that they also say that in an open system the X-order cannot increase faster than it is imported through the boundary. Thus the equations for entropy change do not support the illogical ‘‘compensation’’ idea; instead, they illustrate the tautology that ‘‘if an increase in order is extremely improbable when a system is closed, it is still extremely improbable when the system is open, unless something is entering which makes it not extremely improbable’’. Thus, unless we are willing to argue that the influx of solar energy into the Earth makes the appearance of spaceships, computers and the Internet not extremely improbable, we have to conclude that the second law has in fact been violated here.