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Information Pressure in Quantum Matter (IPQM)

Jincheng Zhang

Published Aug 19, 2026• 0 citations
Publisher

Abstract

In the realm of condensed matter physics, the interplay between quantum information and material properties has emerged as a fertile area of inquiry. Here we propose a novel conceptual framework, termed Information Pressure in Quantum Matter (IPQM), in which changes in the informational state of a quantum system generate an effective mechanical pressure, P_I, that influences the energetic landscape and phase stability of the material. We formulate a quantitative description of P_I based on the von Neumann entropy, S = -Tr(ρ ln ρ), of the reduced density matrix ρ associated with a subsystem. The effective pressure is defined as P_I = -k_B T (∂S/∂V)_T, where V is the volume of the subsystem and T is the temperature. By coupling P_I to the conventional Gibbs free energy, G = U - TS + PV, we derive modified equations of state that predict shifts in critical points and the emergence of new phases when the system undergoes controlled information manipulation. We illustrate the utility of IPQM with several theoretical examples, including spin chains, topological insulators, and superconducting lattices, where information-driven perturbations can tune magnetic ordering, band topology, and pairing symmetry. The IPQM framework provides a unified language for describing how information processing operations, such as unitary gates, measurements, and error correction, can be leveraged to engineer quantum matter with desired properties. This perspective opens pathways toward the design of pressure-free, information-controlled quantum devices and suggests a new class of quantum thermodynamic cycles that exploit information flow as a resource.

DOI
10.5281/zenodo.22005322

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In the realm of condensed matter physics, the interplay between quantum information and material properties has emerged as a fertile area of inquiry. Here we propose a novel conceptual framework, termed Information Pressure in Quantum Matter (IPQM), in which changes in the informational state of a quantum system generate an effective mechanical pressure, P_I, that influences the energetic landscape and phase stability of the material. We formulate a quantitative description of P_I based on the von Neumann entropy, S = -Tr(ρ ln ρ), of the reduced density matrix ρ associated with a subsystem. The effective pressure is defined as P_I = -k_B T (∂S/∂V)_T, where V is the volume of the subsystem and T is the temperature. By coupling P_I to the conventional Gibbs free energy, G = U - TS + PV, we derive modified equations of state that predict shifts in critical points and the emergence of new phases when the system undergoes controlled information manipulation. We illustrate the utility of IPQM with several theoretical examples, including spin chains, topological insulators, and superconducting lattices, where information-driven perturbations can tune magnetic ordering, band topology, and pairing symmetry. The IPQM framework provides a unified language for describing how information processing operations, such as unitary gates, measurements, and error correction, can be leveraged to engineer quantum matter with desired properties. This perspective opens pathways toward the design of pressure-free, information-controlled quantum devices and suggests a new class of quantum thermodynamic cycles that exploit information flow as a resource.
The intersection of information theory and fundamental physics has traditionally centered on the thermodynamic cost of computation, entropy bounds, and the informational interpretation of quantum states. This paper introduces the theoretical framework of Negative Information Pressure (NIP), positing that high-density quantum information structures exert an effective mechanical and thermodynamic force analogous to pressure. By defining an information energy term proportional to the quantum information complexity of a system, denoted as E_I = \lambda * I(\rho), we derive an explicit formulation for negative information pressure as the negative partial derivative of information energy with respect to system volume, P_I = -(\partial E_I) / (\partial V). This framework bridges the conceptual gap between abstract information configurations and concrete physical dynamics, suggesting that highly compressed, entangled, or structured quantum states can actively modify local boundary responses and macroscopic forces without requiring classical particle interactions. The implications of this paradigm extend the foundational motto of information physics into a dynamic realm where information directly governs physical evolution, offering new theoretical perspectives for quantum thermodynamics and information-driven physical systems.
In conventional condensed‑matter physics, transport phenomena are usually described by electric current J_E and heat current J_Q, each associated with the flow of charge or energy. In this work we introduce a fundamentally distinct quantity, the internal information current J_I, which characterises the spatial transport of quantum information within a material. By deriving a continuity equation for the local von Neumann entropy density ρ_I and identifying the corresponding flux J_I, we establish a unified framework that connects quantum information theory with transport theory. The formalism naturally incorporates coherence and entanglement as intrinsic sources of information flow, thereby revealing new mechanisms for energy conversion, quantum state control, and material functionality. We discuss potential experimental signatures in ultracold atomic lattices, solid‑state qubits, and topological insulators, and outline the implications for quantum thermodynamics, quantum sensing, and the design of next‑generation quantum devices. This novel perspective offers a pathway toward harnessing information as a physical resource in quantum matter, with prospective relevance to the Nobel‑level discovery of quantum materials that bridge information and matter.
This paper introduces the Quantum Entanglement Pressure Effect (QEPE), a theoretical framework in which quantum entanglement modifies the effective mechanical pressure of a system. We formalize the relation PE=f(SE)P_E = f(S_E)PE​=f(SE​), where PEP_EPE​ denotes the entanglement‑induced pressure correction and SES_ESE​ is the entanglement entropy shared among subsystems. By integrating entanglement contributions into the stress–energy tensor, we derive modified equations of state for many‑body quantum systems. The analysis predicts measurable shifts in equilibrium volumes, elastic moduli, and critical points in quantum materials such as topological insulators and unconventional superconductors. We discuss the macroscopic implications of QEPE, its potential to reveal new phases of matter, and the prospect of experimental verification using high‑precision calorimetry and pressure‑dependent spectroscopy. Finally, we argue that the discovery of a macroscopic entanglement‑driven pressure effect could constitute a landmark in condensed‑matter physics, warranting recognition at the highest levels, including the Nobel Prize.
The transport properties of condensed matter are traditionally described in terms of charge currents, spin currents, and heat currents, each associated with a distinct flux of physical quantities. In this work we introduce a new concept, the internal information flow, denoted by J_I, which quantifies the rate of change of quantum information residing within a material system. Unlike conventional currents, J_I is not directly associated with a conserved charge or energy but rather with the redistribution of correlations and entanglement among the degrees of freedom. We formulate J_I in a rigorous operator framework, show that it obeys continuity-like equations, and illustrate its distinct physical consequences through several model systems. We further discuss possible measurement schemes based on quantum tomography and weak measurement techniques, and highlight the potential of internal information flow to bridge quantum information science and materials physics. The theoretical framework presented here opens a new avenue for exploring quantum thermodynamics, quantum phase transitions, and ultimately paves the way for a deeper understanding of the interplay between information and matter.
The concept of quantum entanglement has been central to the development of quantum information theory, yet its influence on macroscopic thermodynamic quantities remains largely unexplored. In this paper, we introduce the Quantum Entanglement Pressure Effect (QEPE), a theoretical framework that links the amount of entanglement present in a quantum system to its effective mechanical pressure. We propose that the pressure contributed by entanglement, denoted P_E, is a function of the system's entanglement entropy, S_E, according to the relation P_E = f(S_E). By constructing a microscopic model of interacting spin‑½ particles with an entanglement‑dependent interaction term, we derive an explicit form for f(S_E) and discuss its physical interpretation. The QEPE has potential implications for the design of quantum materials, the control of phase transitions, and the emergence of macroscopic quantum effects that could be relevant to high‑temperature superconductivity and quantum thermodynamics. This theoretical exploration opens new avenues for experimental investigation in quantum materials and may provide a pathway toward a Nobel‑level discovery of entanglement's macroscopic influence.
The notion of information in quantum mechanics has traditionally been viewed through the lens of entropy, mutual information, and measurement back‑action. In this work we introduce a new concept, Quantum Measurement Information Pressure (QMIP), which quantifies the effective mechanical or energetic pressure exerted by the informational change that occurs during a quantum measurement. QMIP is defined as the derivative of the measurement‑induced informational entropy with respect to an effective measurement volume or a parameter that governs the coupling between the system and the measuring apparatus. We present a detailed mathematical formulation of QMIP, discuss its physical interpretation in terms of work extraction and feedback control, and outline potential experimental realizations in quantum feedback systems. By bridging the gap between information theory and physical forces at the quantum scale, QMIP offers a fresh perspective on the thermodynamic cost of quantum measurement and suggests pathways towards high‑impact applications, possibly deserving recognition at the Nobel level.