# Almost Markovian processes from closed dynamics

Pedro Figueroa-Romero, Kavan Modi, and Felix A. Pollock

School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia

### Abstract

It is common, when dealing with quantum processes involving a subsystem of a much larger composite closed system, to treat them as effectively memory-less (Markovian). While open systems theory tells us that non-Markovian processes should be the norm, the ubiquity of Markovian processes is undeniable. Here, without resorting to the Born-Markov assumption of weak coupling or making any approximations, we formally prove that processes are close to Markovian ones, when the subsystem is sufficiently small compared to the remainder of the composite, with a probability that tends to unity exponentially in the size of the latter. We also show that, for a fixed global system size, it may not be possible to neglect non-Markovian effects when the process is allowed to continue for long enough. However, detecting non-Markovianity for such processes would usually require non-trivial entangling resources. Our results have foundational importance, as they give birth to $\textit{almost}$ Markovian processes from composite closed dynamics, and to obtain them we introduce a new notion of equilibration that is far stronger than the conventional one and show that this stronger equilibration is attained.

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### Cited by

[1] Lars Knipschild and Jochen Gemmer, "Modern concepts of quantum equilibration do not rule out strange relaxation dynamics", Physical Review E 101 6, 062205 (2020).

[2] Pedro Figueroa-Romero, Kavan Modi, and Felix A. Pollock, "Equilibration on average in quantum processes with finite temporal resolution", Physical Review E 102 3, 032144 (2020).

[3] Philip Taranto, "Memory effects in quantum processes", International Journal of Quantum Information 18 02, 1941002 (2020).

[4] Kavan Modi, "George Sudarshan and Quantum Dynamics", Open Systems & Information Dynamics 26 03, 1950013 (2019).

[5] Aidan Strathearn, Springer Theses 99 (2020) ISBN:978-3-030-54974-9.

[6] Aidan Strathearn, Springer Theses 1 (2020) ISBN:978-3-030-54974-9.

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