The thermodynamics of writing a random polymer.

T he notion that information has physical, and in particular, thermodynamic, content can be traced to the paradox of Maxwell’s demon, a sly creature who observes the microscopic motions of gas particles on both sides of a partition (1). By controlling a trap door the demon segregates fast particles from slow ones to create a temperature difference across the partition, seemingly without expending any work. Generations of physicists have scratched their heads over this apparent violation of the second law of thermodynamics (2–5). The resolution that has eventually emerged acknowledges that a real-life Maxwell’s demon—say, a nanoscale machine designed for the task—collects information as it operates, and work must be expended to erase this information, otherwise the demon’s memory banks fill up. The minimum work required is kBT ln 2 per bit of information, precisely what is needed to rescue the second law from the paradox. In this issue of PNAS, Andrieux and Gaspard (6) analyze the flip side of the thermodynamic cost of information erasure; namely, the cost of information acquisition. The setting of their analysis is not a demon and a gas, but rather a process essential to living organisms: copolymerization, in which a chain-like molecule grows by the addition of chemically distinct units (monomers). The most celebrated example is the replication of DNA, by which genetic information is copied at the molecular level, ultimately to pass down the generations of a family tree. Noting that copolymerization is a physical process ‘‘ruled by the statistical laws of motion and thermodynamics,’’ Andrieux and Gaspard (6) set out to investigate the implications of these laws, focusing on the interplay between the information that gets stored in the sequence of monomers (e.g., the pattern of nucleotides A, G, C, and T in the case of DNA) and the thermodynamic forces that drive the copolymerization process. As a warm-up problem, they first consider polymer growth without a template. Imagine a solution containing an alphabet soup of monomer species, in which floats a single chain of length l, with chemical bonds linking adjacent units. This polymer can grow by a reaction that attaches a new monomer to its end or shrink by the reverse reaction, in which a monomer drops back into the solution. We further imagine that the concentrations of the free monomer species in solution are kept fixed by an external agent that pumps them into or out of solution as necessary. In this situation, the polymer might reach a nonequilibrium stationary state in which it grows at an average rate v dl/dt 0,