Variational nonequilibrium thermodynamics of reaction-diffusion systems. I. The information potential

In this work, we consider the nonequilibrium thermodynamics of a reaction-diffusion system at a given temperature, using the Master equation. The information potential is defined as the logarithm of the stationary state. We compare the approximations, given by the Fokker-Planck equation and the Wentzel-Kramers-Brillouin method directly applied to the Master equation, and prove that they lead to very different results. Finally, we show that the information potential satisfies a Hamilton-Jacobi equation and deduce general properties of this potential, valid for any reaction-diffusion system, as well as a unicity result for the regular solution of the Hamilton-Jacobi equation. A second article (Paper II), in the same series, will develop a path integral approach and an estimation of the chemical rate constants in this general context. (C) 1999 American Institute of Physics. [S0021-9606(99)50940-9].