Heat current and entropy production rate in local non-Markovian quantum dynamics of global Markovian evolution

Entropy Production in Non-Markovian Collision Models: Information Backflow vs. System-Environment Correlations

“…We follow a discretization approach for the time derivative of the entropy production similar to what we have done for the time derivative of the trace distance in the non-Markovianity measure calculation, and write it as The entropy production rate is always a positive quantity for Markovian dynamics due to the Spohn’s inequality [ 33 ], which can also be seen from the fact that quantum relative entropy is a non-increasing function under completely positive trace preserving (CPTP) maps [ 42 ]. However, for non-Markovian dynamics, it has been shown in a number of works that the entropy production rate can attain negative values throughout the transient dynamics [ 17 , 18 , 19 , 20 , 21 , 22 , 23 , 26 , 27 ]. In fact, in the vast majority of these studies, the negativity of the entropy production rate is claimed to be linked to the presence of memory effects due to non-Markovianity.…”

“…In particular, we are interested in the relationship between non-Markovianity and the irreversible entropy production during open system dynamics, which has been a topic of intense debate over the last years [ 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ] and naturally extends to the discussions on the violations of the Landauer bound [ 28 , 29 , 30 , 31 , 32 ]. It is a well-established fact that Markovian quantum dynamics, which can be described by a completely positive trace preserving (CPTP) map, lead to a positive rate of entropy production as proven by Spohn’s inequality [ 33 ].…”

Dynamics of a quantum interacting system -Extended Global Approach beyond the Born-Markov and secular approximation

“…However, the non-Markovian dynamics for the GA have been mainly analyzed under the SA in [65][66][67][68]. We find recent analyses going beyond the SA in [69,70] enabling a comparison of the exact solutions of the Green function [69] and the exact numerical solution [70].…”