Structural Theory of Information Backflow in Non-Markovian Relaxation: TC/TCL Formalism and Minimal Phase Diagrams
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914320880762880 |
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| author | Nakagawa, Koichi |
| author_facet | Nakagawa, Koichi |
| contents | We develop a structural theory of information backflow in minimal non-Markovian relaxation processes within the framework of nonequilibrium statistical mechanics. The approach is based on the time-convolution (TC) and time-convolutionless (TCL) projection-operator formalisms for reduced dynamics and on the doubling construction of non-equilibrium thermo field dynamics, which provides an embedding representation of dissipative evolution.
We introduce a general backflow functional associated with a time-dependent information measure and derive generator-based sufficient conditions for the absence of backflow in terms of divisibility properties and effective relaxation rates. This allows a direct connection between memory kernels in generalized master equations and observable transient phenomena such as entropy overshoot and revival.
Furthermore, we propose a decomposition of backflow into classical mixing and intrinsic contributions in the doubled representation, leading to a unified classification of transient regimes. Minimal classical and quantum two-state models are analyzed as analytically tractable examples, yielding explicit phase diagrams and recovering Mittag-Leffler-type fractional relaxation as a universal envelope of non-Markovian damping.
The framework provides a constructive TC-to-TCL procedure for extracting effective rates and organizing memory-induced phenomena in a model-independent manner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09054 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Structural Theory of Information Backflow in Non-Markovian Relaxation: TC/TCL Formalism and Minimal Phase Diagrams Nakagawa, Koichi Quantum Physics Statistical Mechanics We develop a structural theory of information backflow in minimal non-Markovian relaxation processes within the framework of nonequilibrium statistical mechanics. The approach is based on the time-convolution (TC) and time-convolutionless (TCL) projection-operator formalisms for reduced dynamics and on the doubling construction of non-equilibrium thermo field dynamics, which provides an embedding representation of dissipative evolution. We introduce a general backflow functional associated with a time-dependent information measure and derive generator-based sufficient conditions for the absence of backflow in terms of divisibility properties and effective relaxation rates. This allows a direct connection between memory kernels in generalized master equations and observable transient phenomena such as entropy overshoot and revival. Furthermore, we propose a decomposition of backflow into classical mixing and intrinsic contributions in the doubled representation, leading to a unified classification of transient regimes. Minimal classical and quantum two-state models are analyzed as analytically tractable examples, yielding explicit phase diagrams and recovering Mittag-Leffler-type fractional relaxation as a universal envelope of non-Markovian damping. The framework provides a constructive TC-to-TCL procedure for extracting effective rates and organizing memory-induced phenomena in a model-independent manner. |
| title | Structural Theory of Information Backflow in Non-Markovian Relaxation: TC/TCL Formalism and Minimal Phase Diagrams |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2602.09054 |