The coupling of density and internal energy fluctuations by isothermal chemical reactions

Under nonequilibrium conditions chemical reactions can modify the coupling of fluctuations in number densities to fluctuations in the internal energy. At a nonequilibrium steady state these fluctuations renormalize the intensive thermodynamic variables, including the temperature and chemical potentials, so that they no longer have their local equilibrium form. Using the mechanistic statistical theory of nonequilibrium thermodynamics, we show at an isothermal steady state that the chemical reaction X+Y⇄2X provides a nonequilibrium coupling of the density and internal energy fluctuations. If thermal exchange with the reservoir is rapid, this coupling can be small, but only under specific conditions such as occur in dilute solution. Under such conditions the steady state temperature is identical to the Kelvin temperature and the density fluctuations are those calculated by treating the temperature as a fixed parameter. The steady state thermodynamics of the dilute, isothermal reactive system is discussed.