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postulated, real physical world of ever-increasing entropy. He showed that at an absolute temperature of zero, entropy is zero. We can illustrate an approach to this singular state by placing a heated metal rod in ice water which would result in a decrease in the entropy of the rod’s molecular motions by dQ/ T₁ < 0, the cooling reducing the complexity of molecular motion in the metal bar and an increase in the entropy of the water by dQ/T₂ > 0 indicating an increase in the amount and complexity of the surrounding water’s molecular motions. Of course the heat moves from metal rod to the water as T₁ →T₂ making dQ > 0 positive and the entropy change, dS = dQ/ T₂ - dQ/ T₁, also positive. In another simple example, producing friction by rubbing a surface generates heat, dQ > 0, at a temperature T. This induces a positive change in entropy, dQ/ T > 0, in the form of increasing amount and complexity of the patterns of molecular motion in the air surrounding the rubbed surface.

Using another related and well-known thermodynamic thought toy, the original isolated, insulated body of gas in the cylinder is partitioned by a membrane into two chambers, one containing all the gas with its temperature, pressure and ability to do mechanical work and the other a vacuum without these properties. This equilibrium state is changed into another equilibrium state by suddenly removing the membrane, filling both chambers with gas and, while increasing its entropy irreversibly, dS > 0, removes at least some of the gas’s ability to do piston raising work. In the context of classical thermodynamics, it is in this way that irreversibility can be defined by its associated increase in entropy. Though there has been no change in total energy in this insulated closed system, an increase in entropy means a decrease of the energy available for work. The increased disorder in the gas is associated with the loss of ability to convert heat, thermal energy, into mechanical energy. Historically important and still available elementary texts by Enrico Fermi (1936), Mark Zemansky (1957) and Herbert Callen (1985), among many others, explicate clearly the formal, but far from biologically relevant, classical theory of the physical entropy of closed equilibrium thermodynamic systems.

Growing in part out of the formal thermodynamics of physics, statistical mechanics offers yet another set of intuitions about the not-necessarily-known

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