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Entropy
Volume 27
Issue 12
10.3390/e27121207
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Article

Physical Origins of Memory Effects in a Non-Markovian Quantum Evolution

by
Shao-Cheng Hou
1,*,
Yu-Han Zhou
1,
Xing-Yuan Zhang
1 and
Xue-Xi Yi
2,*
1
School of Science, Dalian Maritime University, Dalian 116026, China
2
Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China
*
Authors to whom correspondence should be addressed.
Entropy 2025, 27(12), 1207; https://doi.org/10.3390/e27121207 (registering DOI)
Submission received: 10 November 2025 / Revised: 23 November 2025 / Accepted: 25 November 2025 / Published: 27 November 2025
(This article belongs to the Special Issue Non-Markovian Open Quantum Systems)
Versions Notes

Abstract

We quantitatively investigate the physical origins of the non-Markovianity measure proposed in our previous work, which can be directly interpreted as memory effects, i.e., the dependence of a quantum system’s future evolution on its history. Using the properties of the trace norm and the trace distance, we find that the strength of memory effects in an evolution is upper (lower) bounded by the sum (difference) of two quantities. One originates from (bounded by) the change of environment state caused by the system, the other from (bounded by) the correlations between the system and the environment. The simulation results for the Jaynes–Cummings model show that the two origins may contribute to the memory effects in different manners, depending on the initial states of the environment and the system.
Keywords: memory effects; system–environment correlations; non-Markovian quantum dynamics; non-Markovianity; Jaynes–Cummings model memory effects; system–environment correlations; non-Markovian quantum dynamics; non-Markovianity; Jaynes–Cummings model

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MDPI and ACS Style

Hou, S.-C.; Zhou, Y.-H.; Zhang, X.-Y.; Yi, X.-X. Physical Origins of Memory Effects in a Non-Markovian Quantum Evolution. Entropy 2025, 27, 1207. https://doi.org/10.3390/e27121207

AMA Style

Hou S-C, Zhou Y-H, Zhang X-Y, Yi X-X. Physical Origins of Memory Effects in a Non-Markovian Quantum Evolution. Entropy. 2025; 27(12):1207. https://doi.org/10.3390/e27121207

Chicago/Turabian Style

Hou, Shao-Cheng, Yu-Han Zhou, Xing-Yuan Zhang, and Xue-Xi Yi. 2025. "Physical Origins of Memory Effects in a Non-Markovian Quantum Evolution" Entropy 27, no. 12: 1207. https://doi.org/10.3390/e27121207

APA Style

Hou, S.-C., Zhou, Y.-H., Zhang, X.-Y., & Yi, X.-X. (2025). Physical Origins of Memory Effects in a Non-Markovian Quantum Evolution. Entropy, 27(12), 1207. https://doi.org/10.3390/e27121207

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