We explore the consequences of metrically decomposing a finite phase space, modeled as a d-dimensional lattice, into disjoint\r\nsubspaces (lattices). Ergodic flows of a test particle undergoing an unbiased random walk are characterized by implementing\r\nthe theory of finite Markov processes. Insights drawn from number theory are used to design the sublattices, the roles of lattice\r\nsymmetry and system dimensionality are separately considered, and new lattice invariance relations are derived to corroborate the\r\nnumerical accuracy of the calculated results.We find that the reaction efficiency in a finite system is strongly dependent not only on\r\nwhether the system is compartmentalized, but also on whether the overall reaction space of the microreactor is further partitioned\r\ninto separable reactors.We find that the reaction efficiency in a finite system is strongly dependent not only on whether the system\r\nis compartmentalized, but also on whether the overall reaction space of the microreactor is further partitioned into separable\r\nreactors. The sensitivity of kinetic processes in nanoassemblies to the dimensionality of compartmentalized reaction spaces is\r\nquantified.
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