Embedding non-Markovian Langevin dynamics into Markovian form with auxiliary variables produces a unique, monotonically increasing Markovian entropy production for the original system.
Zwanzig, Memory Effects in Irreversible Thermody- namics, Physical Review124, 983 (1961)
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Markovian thermodynamics of non-Markovian Langevin equations
Embedding non-Markovian Langevin dynamics into Markovian form with auxiliary variables produces a unique, monotonically increasing Markovian entropy production for the original system.