Entropy is a fundamental quantity in both classical and quantum physics, usually regarded as a scalar measure of disorder or uncertainty. In this work we propose a novel viewpoint: the existence of an entropy flow field in quantum systems, denoted by J_S(x,t). This field, analogous to the conventional heat current, encapsulates the spatiotemporal transport of informational entropy within a many‑body wavefunction or density matrix. We develop a rigorous mathematical framework for J_S(x,t), derive its properties from the Lindblad master equation, and discuss how it unifies concepts from quantum thermodynamics and quantum information theory. The core contribution is a practical imaging protocol—Quantum Entropy Flow Imaging (QEFI)—that reconstructs the spatial distribution of J_S(x,t) from measurable observables in quantum simulators or engineered quantum devices. The method offers a new diagnostic tool for exploring nonequilibrium dynamics, entanglement propagation, and thermalization pathways. Potential applications range from characterizing heat transport in ultracold gases to optimizing quantum control protocols in noisy intermediate‑scale quantum processors.
Entropy is a fundamental quantity in both classical and quantum physics, usually regarded as a scalar measure of disorder or uncertainty. In this work we propose a novel viewpoint: the existence of an entropy flow field in quantum systems, denoted by J_S(x,t). This field, analogous to the conventional heat current, encapsulates the spatiotemporal transport of informational entropy within a many‑body wavefunction or density matrix. We develop a rigorous mathematical framework for J_S(x,t), derive its properties from the Lindblad master equation, and discuss how it unifies concepts from quantum thermodynamics and quantum information theory. The core contribution is a practical imaging protocol—Quantum Entropy Flow Imaging (QEFI)—that reconstructs the spatial distribution of J_S(x,t) from measurable observables in quantum simulators or engineered quantum devices. The method offers a new diagnostic tool for exploring nonequilibrium dynamics, entanglement propagation, and thermalization pathways. Potential applications range from characterizing heat transport in ultracold gases to optimizing quantum control protocols in noisy intermediate‑scale quantum processors.
The concept of entropy is central to both classical thermodynamics and quantum information science. In conventional treatments, entropy is a scalar quantity associated with a statistical ensemble or a quantum state. This paper introduces a novel perspective in which quantum systems support an entropy flow field, denoted J_S(x,t), analogous to the heat current in classical thermodynamics. We develop a rigorous theoretical framework for defining and calculating entropy flow in closed and open quantum systems, and we propose a method for imaging this flow by mapping local entropy production rates onto spatial coordinates. The resulting Quantum Entropy Flow Imaging (QEFI) technique offers a powerful diagnostic tool for probing nonequilibrium quantum dynamics, revealing hidden structure in entanglement propagation, and bridging the gap between quantum information and thermodynamic concepts. While the experimental implementation of QEFI is left for future work, we outline how quantum simulators and ultracold atomic gases can be employed to test the predictions. The potential to observe entropy currents in quantum devices opens new avenues for exploring fundamental questions about the nature of entropy, information flow, and their role in quantum technologies.
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.
A central open question in quantum thermodynamics is the identification of thermodynamic entropy away from equilibrium. Although thermodynamic entropy coincides with the von Neumann entropy for a Gibbs state at equilibrium, the thermodynamic role of quantum coherence generated during nonequilibrium evolution remains unclear. Here, we show that von Neumann entropy does not, in general, represent the thermodynamic entropy governing heat exchange in coherent nonequilibrium quantum systems. By integrating the resource theory of quantum coherence with thermodynamic principles, we develop a general framework for nonequilibrium quantum thermodynamics. We identify thermodynamic entropy with the energy entropy derived from energy-measurement statistics and introduce a dynamical temperature extending the equilibrium concept to nonequilibrium states. Consequently, we obtain an exact entropy-balance relation separating the entropy flux associated with heat exchange from the coherence-loss contribution to entropy production, establishing an operational connection between quantum coherence, heat flow, and total entropy change. Unlike approaches relying on equilibrium reference states or stationary Gibbs ensembles, our framework uses instantaneous dynamical quantities and remains valid throughout transient nonequilibrium evolution. It provides consistent dynamical definitions of temperature, work, heat, and free energy. Applying the formalism to an exactly solvable open quantum system, we show that the first and second laws hold throughout transient evolution and that equilibrium thermodynamics emerges dynamically in the weak-coupling long-time limit. Our results establish a unified framework for coherent nonequilibrium quantum thermodynamics and suggest opportunities for controlling heat dissipation through coherence engineering in quantum thermal technologies.
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 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 QT, 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 QT 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 QT 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.
This paper presents a comprehensive exposition of quantum thermodynamics, aiming to bridge the foundational concepts of classical thermodynamics and quantum mechanics.Beginning with a rigorous overview of classical thermodynamic laws and statistical ensembles, the work transitions into the quantum domain by introducing quantum states, density operators, and von Neumann entropy.Core thermodynamic quantities such as work, heat, energy, and entropy are redefined in the quantum regime, with emphasis on operational frameworks like the twopoint measurement scheme.The study explores the role of quantum resource theories in formulating generalizations of the second law and delves into the intricacies of nonequilibrium thermodynamics through fluctuation theorems, such as the Jarzynski equality and Crooks theorem.Special attention is given to the influence of coherence, entanglement, and measurement backaction, which contribute uniquely to quantum thermodynamic behavior.The treatise concludes with a discussion on quantum heat engines, thermodynamic consistency of quantum master equations, and information-theoretic approaches, establishing quantum thermodynamics as a vital framework for understanding energy and information flow at the quantum scale.