Stochastic Matrix Product States

TL;DR

This paper introduces stochastic matrix product states, defining a new correlation measure called entropy cost, and demonstrates its application to steady states in non-equilibrium stochastic processes like the asymmetric exclusion process.

Contribution

It presents the concept of stochastic matrix product states, introduces the entropy cost as a correlation measure, and applies these ideas to non-equilibrium steady states.

Findings

Defined stochastic matrix product states for steady states.

Introduced entropy cost as a correlation measure.

Applied framework to asymmetric exclusion process.

Abstract

The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows to define the analogue of Schmidt coefficients for steady states of non-equilibrium stochastic processes. We discuss a new measure for correlations which is analogous to the 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 hand of the asymmetric exclusion process.