We apply the eikonal approximation to the stochastic master equation for reaction−diffusion systems. Its stationary solution is expressed as an excess work and is shown to be a Lyapunov function for the deterministic evolution of inhomogeneous systems. From this result we establish a new stochastic criterion of relative stability and equistability of systems with multiple homogeneous stationary states in terms of inhomogeneous fluctuations.
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Hansen et al. (1998) studied this question.
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