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 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.
Highlights
The quest towards understanding how thermodynamics emerges from quantum theory has seen a great deal of recent progress [1, 2]
The conundrum of how to recover irreversible phenomena that obey the second law of thermodynamics, starting from reversible and recurrent Schrödinger dynamics, has been rectified by considering an analogous dynamical equilibrium
For the class of evolutions given by the Haar measure, above a critical time scale the dynamics of a subsystem is exponentially close to a Markov process as a function of the relative size of the subsystem compared with the whole
Summary
The quest towards understanding how thermodynamics emerges from quantum theory has seen a great deal of recent progress [1, 2]. The standard approach to making this approximation in open quantum systems theory involves a series of assumptions about weak interactions with an environment sufficiently large and ergodic that the memory of past interactions gets practically lost [7, 8]; this is mathematically equivalent (through an analogue of Stinespring’s dilation theorem) to continually refreshing (discarding and replacing) the environment’s state [9], i.e., artificially throwing away information from the environment (see Fig. 2) In reality, this is not usually how a closed system evolves, leading to the question: In the general case, how does dissipative Markovian dynamics emerge from closed Schrödinger evolution? It allows for a precise quantification of memory effects (including across multiple time points) [5], that we employ here as a natural setting to explore temporal correlations and the role that they play in a generalized, or strong, notion of equilibration
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
