Structural Theory of Information Backflow in Non-Markovian Relaxation: TC/TCL Formalism and Minimal Phase Diagrams

• URL: http://arxiv.org/abs/2602.09054v2
• Date: Wed, 11 Feb 2026 07:08:45 GMT
• Title: Structural Theory of Information Backflow in Non-Markovian Relaxation: TC/TCL Formalism and Minimal Phase Diagrams
• Authors: Koichi Nakagawa,
• Abstract summary: We develop a structural theory of information backflow in minimal non-Markovian relaxation processes.<n>The framework provides a constructive TC-to-TCL procedure for extracting effective rates and organizing memory-induced phenomena.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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