The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows us to define the analogue of Schmidt coefficients for steady states of nonequilibrium stochastic processes. We discuss a new measure for correlations which is analogous to entanglement entropy, the entropy cost $S_C$, and show that this measure quantifies the bond dimension needed to represent a steady state as a matrix product state. We illustrate these concepts on the basis of the asymmetric exclusion process.

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