Thermodynamics of computing: Entropy of nonergodic systems

Landauer discussed the minimum energy necessary for computation and stated that erasure of information is accompanied with kT ln 2/ bit of heat generation. We reconsider this problem on the basis of Clausius's equation defining the thermodynamic entropy. We show that the erasing process, involving a transition from a nonergodic to an ergodic state, is irreversible and accompanied with k ln 2/bit of entropy generation, while the heat generation occurs in a writing process. The inverse of the erasing process corresponds to spontaneous symmetry breaking from an ergodic to a nonergodic state, which induces a decrease(!) in thermodynamic entropy. Our theory is examined by a simulation of a binary device described by a Langevin equation. We argue that the so-called residual entropy of symmetry broken states, such as in ice, is not a thermodynamic quantity, even if it might be called "information entropy." (c) 2001 American Institute of Physics.