The motion of electrons in atomic and molecular orbitals is traditionally associated with the generation of electric current, denoted by J_e, arising from the transport of charge. In this work we propose a complementary concept, the Orbital Information Current (OIC), represented by J_I, which captures the flow of quantum information inherent in the spatial distribution of the electronic wavefunction. By extending the continuity equation to encompass the probability density associated with an orbital, we derive an explicit expression for J_I in terms of the real and imaginary components of the wavefunction. This formulation reveals that information propagation is intrinsically tied to the phase gradient of the orbital, independent of charge transport. We discuss the physical significance of J_I, outline potential experimental scenarios in two‑dimensional quantum materials where information currents could be measured, and suggest that OIC provides a foundational element for the emerging field of "information physics." No experimental data are presented; the paper is purely theoretical.
The motion of electrons in atomic and molecular orbitals is traditionally associated with the generation of electric current, denoted by J_e, arising from the transport of charge. In this work we propose a complementary concept, the Orbital Information Current (OIC), represented by J_I, which captures the flow of quantum information inherent in the spatial distribution of the electronic wavefunction. By extending the continuity equation to encompass the probability density associated with an orbital, we derive an explicit expression for J_I in terms of the real and imaginary components of the wavefunction. This formulation reveals that information propagation is intrinsically tied to the phase gradient of the orbital, independent of charge transport. We discuss the physical significance of J_I, outline potential experimental scenarios in two‑dimensional quantum materials where information currents could be measured, and suggest that OIC provides a foundational element for the emerging field of "information physics." No experimental data are presented; the paper is purely theoretical.
The motion of electrons in a quantum system is traditionally described in terms of charge transport, yielding an electric current density J_e. In this work we propose that the same quantum mechanical motion also carries an intrinsic information flow, denoted J_I, which quantifies the propagation of the quantum state's informational content through space and time. We develop a formalism in which the orbital probability density ρ(r, t) and its associated phase θ(r, t) give rise to two coupled continuity equations: one for charge and one for information. The information current is expressed in terms of gradients of the phase and the logarithm of the amplitude of the wavefunction, thereby revealing a direct link between the spatial structure of the orbital and the distribution of quantum information. The framework is applied to two-dimensional quantum materials, where the interplay between electronic band topology and information flow opens avenues for designing devices that manipulate information without dissipative charge transport. The concept of orbital information current lays the foundation for an emerging discipline, "information physics," which seeks to harness quantum informational degrees of freedom for practical applications.
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.
Electronic structure in solids is traditionally described by the distribution of electron energies and the occupation of momentum states. In many-body systems, however, the reorganization of electrons among atomic orbitals can occur without a corresponding change in total electronic energy, yet it may entail a profound rearrangement of quantum correlations and information content. This paper introduces the concept of orbital entropy, a measure of the quantum informational disorder associated with the occupation of local orbital degrees of freedom, and defines its dynamical counterpart, the orbital entropy flow J_S^{orb}. We formulate a continuity equation that couples J_S^{orb} to the orbital current operator, and demonstrate that this flow is distinct from conventional energy and charge currents. The formalism is applied to model Hamiltonians relevant to Mott insulators and Hund's metals, revealing that orbital entropy can be selectively pumped by external fields and that its redistribution governs the temperature dependence of transport coefficients. The existence of a conserved orbital entropy current suggests the possibility of an orbital thermodynamics framework, analogous to conventional thermodynamics but grounded in quantum many-body theory. Potential experimental probes, including ultrafast pump–probe spectroscopy and resonant inelastic X-ray scattering, are discussed as routes to detect J_S^{orb} and to map its spatial variation in correlated crystals. This work opens a new avenue for understanding entropy management in quantum materials and for engineering devices that exploit orbital degrees of freedom for energy conversion and information processing.
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.
The equidensity orbitals (EO) are used in the resultant entropic description of molecular states which combines the probability and current contributions in the overall information content. Continuities of the modulus and phase components of electronic wavefunctions are examined, and the Harriman–Zumbach–Maschke (HZM) construction of Slater determinants yielding the prescribed electron density is explored. The conditional probability interpretation of (complex) HZM wavefunctions is formulated, the entropy/information contributions due to the state phase component are summarized, and a nonclassical origin of quantum dynamics of the resultant gradient information, related to average kinetic energy of electrons, is emphasized. The phase equilibria maximizing the resultant-entropy measures are explored, and “thermodynamic” phase minimizing the overall gradient information is determined. It generates finite orbital currents giving rise to the vanishing resultant flow of electrons in the system as a whole. Potential use of atomic and molecular EO bases in electronic structure calculations and interpretations in chemistry is discussed, and illustrative example of Gaussian probability distribution is examined in some detail.
The need for resultant measures of the Information-Theoretic (IT) content of molecular electronic wavefunctions, combining the information contributions due to the probability and phase/current distributions, is reemphasized. Complementary measures of the state entropy (disorder) and information (order) contents are reexamined, the continuities of wavefunction components are summarized, and the probability acceleration concept is used to determine the current and information sources. The experimental elimination of the state uncertainties is discussed and limitations in this information-acquirement process imposed by the Heisenberg indeterminacy principle are commented upon.