Embedding non-Markovian Langevin dynamics into Markovian form with auxiliary variables produces a unique, monotonically increasing Markovian entropy production for the original system.
Zwanzig, Nonlinear generalized Langevin equations, Journal of Statistical Physics9, 215 (1973)
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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.