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Using the stochastic model of  n -stage first-order reversible chemical reactions, the lifetimes of equilibrium fluctuations about the most probable equilibrium microstate and the times to reach the macroscopic chemical equilibrium are derived. In the latter case, a semistochastic approach (compatible with Schrödinger´s √ N  – rule) and a first-passage time approach are compared. It is shown that for  n  &gt; 2 and large number of reacting particles in the system, the formula for first-passage time can be divided into two parts having a simple physical interpretation: the composition of the system reaches first the boundary of the region of equilibrium fluctuations demarcated by their mean amplitudes (the first term which is identical with the semistochastic formula) and then, after a long random wandering among microstates inside and outside this region, it finally reaches the most probable equilibrium microstate (the second term which is approximately equal to the mean lifetime of system composition fluctuations about the most probable equilibrium microstate). It is concluded that in the case of  n -stage reactions,  n  &gt; 4, the first-passage time approach leads to values of time to reach the equilibrium which correspond from the physical point of view to infinity.

zeitschrift für physikalische chemie

Stochastic Model of the  n -Stage Reversible First-Order Reaction: Relation between the Time of First Passage to the Most Probable Microstate and the Mean Equilibrium Fluctuations Lifetime