A thermodynamic and stochastic study of fluctuations in non-equilibrium open systems displaying phase transitions in steady states

Landau's theory of fluctuations in second-order phase transitions is generalized for non-equilibrium open systems having one degree of freedom and displaying phase-transition-like phenomena in steady states. Taking diffusion into consideration, the fluctuations induce a spatial correlation function p(r,r') of the form (exp-( mod r-r' mod / xi ))/ mod r-r' mod when the situation is simple enough for a correlation length xi to exist. A general formula for xi is obtained. The stochastic master equation is formulated and solved for such systems in the absence of diffusion. Both thermodynamic and stochastic theories are applied to an intrinsic semiconductor model which shows a recombination-induced non-equilibrium phase transition as the external electric field is increased.