Comment: Detailed balance revisited.
The concept of detailed balance is central to the field of chemical kinetics and provides important constraints on relationships between equilibrium and rate constants. Miller et al. [Phys. Chem. Chem. Phys., 2009, 11, 1128] have recently proposed that having the ratio of forward and reverse rate constants equal to the equilibrium constant--a relationship they equate with detailed balance--is a sufficient condition to guarantee that a chemical system eventually relaxes to equilibrium. This assertion is true, however, only for an isolated system. In a closed system, where energy exchange between the system and the environment occurs, input of energy in the form of an externally driven oscillation of a thermodynamic parameter (e.g. pressure or electric field strength), can maintain a chemical system in a stationary state away from equilibrium even if the ratio of the forward and backward rate constants for each elementary reaction equals the equilibrium constant at every instant. This fact allows appropriately designed molecules to serve as free-energy transducers and molecular machines.
Astumian
R Dean
RD
Department of Physics, University of Maine, Orono, Maine 04469-5709, USA. astumian@maine.edu