Information Carriers and Information Theory in Quantum Chemistry.

Shridhar Ramachandra Gadre

Yilin Zhao, Dongbo Zhao, Chunying Rong +2 more

In this survey, we begin with a concise introduction to information theory within Shannon's framework, focusing on the key concept of Shannon entropy and its related quantities: relative entropy, joint entropy, conditional entropy, and mutual information. We then demonstrate how to apply these information-theoretic tools in quantum chemistry, adopting either classical or quantum formalisms based on the choice of information carrier involved.

Lev B. Levitin

Giulio Chiribella, Hlér Kristjánsson

Shannon's theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon theory, explores the new possibilities arising when the information carriers are quantum systems. Traditionally, quantum Shannon theory has focused on scenarios where the internal state of the information carriers is quantum, while their trajectory is classical. Here we propose a second level of quantization where both the information and its propagation in space-time is treated quantum mechanically. The framework is illustrated with a number of examples, showcasing some of the counterintuitive phenomena taking place when information travels simultaneously through multiple transmission lines.

Roman S. Ingarden

Chuanjie Dai

This paper develops a PAC–µ 8 interpretation of the structural unity linking the 2025 Nobel Prize in Physics and the 2025 Nobel Prize in Chemistry. At the level of ordinary disciplinary description, the two prizes concern sharply different domains: macroscopic quantum mechanical tunnelling and energy quantisation in an electric circuit, on the one hand, and the development of metal-organic frameworks (MOFs), on the other. Yet from the perspective of PAC–µ 8 , both achievements instantiate the same underlying generative law. In each case, a carrier is organized by a structured channel, subjected to selective admission and exclusion, stabilized within a constrained regime, and rendered scientifically meaningful through readable output. The central thesis is that these two Nobel-recognized achievements are best understood not as unrelated advances in physics and chemistry, but as two realizations of one structural mother-formula: carrier → structured channel → selective transmission → stabilized occupancy/readout. The superconducting circuit of the physics prize and the porous molecular architecture of the chemistry prize differ in material carrier, local mathematics, and experimental implementation, but they share a common protocol of organized transmission, constrained accessibility, and recoverable record. The paper proceeds in five steps. First, it formulates the PAC–µ 8 conceptual apparatus required for the comparison, emphasizing carrier, channel, boundary, selection, persistence, and certification. Second, it reconstructs the physics prize as a theory of quantum channeling, in which tunnelling and energy quantization are understood as selective-access phenomena within an electrical architecture. Third, it reconstructs the chemistry prize as a theory of molecular channeling, in which pore geometry and framework design define admissible and non-admissible guest behavior. Fourth, it shows that the same mother-formula underlies other apparently unrelated achievements, including filters and adsorbents, cavities and porous rooms, waveguides and membranes, band gaps and pore windows, and qubit readout and chemical sensing. Finally, it argues that PAC–µ 8 offers a comparative ontology in which scientific domains are classified not primarily by what is transported, but by how structure organizes passage. The broader conclusion is that modern science repeatedly discovers the same structural law under different carriers. The significance of the 2025 Nobel prizes therefore extends beyond their local fields. Together they reveal an especially clear example of a deep cross disciplinary unity: structure governs passage, passage governs stability, and stability governs 1what can become scientifically real as a certified record.