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Abstract
The most general exclusion single species reaction–diffusion models are investigated, which are defined on a one-dimensional lattice, have nearest-neighbor interactions, and their corresponding two-site Hamiltonians are diagonalizable or converted to a Jordan form by a direct product of matrices. The diagonalizable Hamiltonians represent a family of 3-parameter stochastic processes, while those which can be transformed into a Jordan form have 4 free parameters. For the diagonalizable Hamiltonians, all of the eigenvalues and eigenvectors and some correlation functions are explicitly calculated. Also, both the entropy and the entropy production rate in such systems are studied. For those Hamiltonians which can be converted to a Jordan form, some parts of the spectrum are obtained.
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