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Physical Information Conservation Search (PICS)

Jincheng Zhang

Published Aug 17, 2026• 0 citations
Publisher

Abstract

The concept of a fundamental conservation law for physical information is introduced. Building on the long‑standing analogy between thermodynamic entropy and Shannon information, we postulate that the total information content of an isolated system, denoted I(t), remains constant over time: I(t)=constant. This proposal is examined in the context of non‑relativistic quantum mechanics and quantum field theory. By constructing an information current and deriving a continuity equation from the Schrödinger equation, we demonstrate that the conservation of I(t) is mathematically consistent with unitary evolution. The implications of this law for the measurement problem, decoherence, and the black‑hole information paradox are discussed. A list of twenty novel research directions that could lead to Nobel‑level breakthroughs is presented, each grounded in a previously unobserved physical observable. The work offers a new perspective that may unify energy, momentum, and information as co‑equal pillars of physical law.

DOI
10.5281/zenodo.21972696

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The concept of a fundamental conservation law for physical information is introduced. Building on the long‑standing analogy between thermodynamic entropy and Shannon information, we postulate that the total information content of an isolated system, denoted I(t), remains constant over time: I(t)=constant. This proposal is examined in the context of non‑relativistic quantum mechanics and quantum field theory. By constructing an information current and deriving a continuity equation from the Schrödinger equation, we demonstrate that the conservation of I(t) is mathematically consistent with unitary evolution. The implications of this law for the measurement problem, decoherence, and the black‑hole information paradox are discussed. A list of twenty novel research directions that could lead to Nobel‑level breakthroughs is presented, each grounded in a previously unobserved physical observable. The work offers a new perspective that may unify energy, momentum, and information as co‑equal pillars of physical law.
The interplay between heat flow and information processing has long been a frontier of both statistical physics and quantum information science. In this work we propose that during thermal evolution of a quantum many‑body system, an otherwise hidden conservation law emerges, which we denote as the Thermal Information Conservation Law (TIC). This law is encapsulated in the invariant quantity QTQ_TQT​, defined as a functional of the system's density matrix and local observables, and remains constant under unitary evolution that couples to a thermal bath only through weak, Markovian channels. The existence of QTQ_TQT​ imposes stringent constraints on the allowed thermal trajectories, thereby providing a new lens through which to view irreversibility, entropy production, and the emergence of classical thermodynamic behavior from quantum dynamics. By establishing a rigorous bridge between the traditional Clausius inequality and a quantum‑information‑theoretic monotone, we demonstrate that TIC can be leveraged to quantify the ultimate limits of heat‑to‑work conversion in quantum engines and to design protocols that suppress entropy generation. The potential Nobel‑worthy significance of this finding lies in its unification of two seemingly disparate domains: the macroscopic laws of thermodynamics and the microscopic rules of quantum information theory. The paper is organized as follows: Section 1 introduces the conceptual framework; Section 2 formalizes the definition of QTQ_TQT​ and proves its conservation under specified conditions; Section 3 discusses the implications for quantum thermodynamics; Section 4 explores connections to quantum information measures such as mutual information and quantum discord; Section 5 outlines theoretical pathways for experimental verification; Section 6 presents a discussion of limitations and future directions; and Section 7 concludes the study.
The deep connection between entropy and information is discussed in terms of both classical and quantum physics. The mechanism of information transfer between systems via entanglement is explored in the context of decoherence theory. The concept of entropic time is then introduced on the basis of information acquisition, which is argued to be effectively irreversible and consistent with both the Second Law of Thermodynamics and our psychological perception of time. This is distinguished from the notion of parametric time, which serves as the temporal parameter for the unitary evolution of a physical state in non-relativistic quantum mechanics. The interpretation of these ideas in terms of both subjective and objective collapse models is also discussed. It is shown that energy is conserved under subjective collapse schemes whereas, in general, under objective collapse it is not. This is consistent with the fact that the latter is inherently non-unitary and that energy conservation arises out of time symmetry in the first place.
The concept of thermal information conservation offers a new perspective on the interplay between thermodynamics and quantum information theory. In this work we introduce the thermal information quantity Q_T, defined for an isolated quantum system as the negative logarithm of the density of states weighted by the Boltzmann factor. We demonstrate that Q_T behaves as a conserved quantity during unitary evolution under a broad class of Hamiltonians that respect a hidden symmetry connecting energy and entropy. By establishing a rigorous link between Q_T and the von Neumann entropy, we show that the standard second law of thermodynamics can be viewed as a special case of a more general conservation principle. The implications of this principle for the design of quantum thermal engines, error‑free quantum memory, and the fundamental limits of heat transport are discussed. The framework also provides a natural bridge between classical thermodynamic irreversibility and quantum reversibility, suggesting that the apparent arrow of time in macroscopic systems may emerge from constraints on Q_T rather than from entropy production alone. Keywords: Thermal information, quantum thermodynamics, conservation law, entropy, quantum engines.
In this article, we discuss through a principle of action the quantum information in relation to the information paradox.The information paradox, which arises in black hole physics, suggests that information can be lost when matter falls into a black hole, which contradicts the principle of information conservation in physics.We propose that the principle of action, which asserts that the action of a physical system is conserved, can be applied to information, showing that information is conserved in a similar way to energy and momentum.Through mathematical models and theoretical analysis, we show that the conservation of information can be understood as a result of the evolution of a system and probability amplitudes in quantum mechanics.
This paper presents a groundbreaking unified framework that bridges quantum information theory and black hole physics by introducing the concept of universal informational phase conservation. Through rigorous simulation of 8-12 qubit systems, we first establish a precise power-law scaling for information leakage: η ∝ N^(-0.43), demonstrating the emergence of near-perfect information conservation in larger quantum systems. A key structural parameter, Δ₀ ≈ 8.0, is identified as the regulator of information flow. We then perform a revolutionary extrapolation, applying this quantum scaling law to resolve the long-standing black hole information paradox. Our model demonstrates that information loss in Hawking radiation becomes negligible (η_BH ~ 10^(-33)) for astrophysical black holes, naturally ensuring information conservation without violating unitarity. The framework is further unified by reinterpreting the consciousness field (from the AOUF v2.5 model) as a cosmic-scale informational phase coordination field (Φ), which governs information dynamics from quantum to cosmic scales. Predictions for anomalous gravitational wave frequency shifts and photon ring brightness enhancements are derived and shown to be consistent with public data from LIGO and the Event Horizon Telescope. This work provides the first quantitative link between microscopic information scaling and macroscopic information paradoxes, offering a testable pathway towards a theory of quantum gravity. Keywords: Information Conservation, Black Hole Information Paradox, Quantum Scaling Laws, Page Curve, Quantum Gravity, Consciousness Field, Δ₀ Parameter, Holographic Principle
We seek to examine the ontological aspects of the resolution of the black hole information paradox. Several concepts which are now central to our understanding of quantum mechanics arose from our resolution to this paradox, and these concepts point to the conservation of all information, even on a quantum level. If quantum information is conserved and can never be erased or destroyed, then this indicates that all information is at least theoretically, ultimately retrievable and knowable from the event horizon of the universe. Ontologically, this supports the contention that a repository of all information in the universe must therefore exist. Herein, we trace the steps in this contention and conclude with the argument that our understanding of the universe points to the existence of an omniscient entity.