Fluctuations and noise in kinetic systems. II. Open ensembles at equilibrium and steady state

We consider the noise and fluctuations of an open ensemble of independent systems each of which can exist in a set of discrete states {0, 1, 2,..., x}. By an open ensemble we mean that the systems in the ensemble may be exchanged with one or more reservoirs. We derive the noise power spectrum of the quantity ${\mathrm{N=\Sigma }}_{\text{i=0}}^x{a}_i{N}_i$ as a function of rate constants of the kinetic rate equations (α_ij for the transition i →j, etc.). N _i is the number of systems of the ensemble in state i and the a _i 's are constants. This paper and a previous one [Y. Chen and T. L. Hill, Biophys. J. (to be published)] form a complete noise analysis for discrete linear kinetic systems and may be used in differentiating various kinetic schemes in complex biological problems. Also obtained is a Poisson distribution function for the number of systems of an open ensemble at cycling steady state (that is, some transition rate constants among the system states do not obey the Wegscheider relation). This extends the usual steady state results on open ensembles in which the Wegscheider relation holds.