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.
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.
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.
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.
Quantum thermodynamics has emerged as a central field for understanding how energy conversion processes occur in microscopic systems. In these systems, effects such as coherence, entanglement, and non-Markovianity play key roles. In this thesis, we explore different ways to describe quantum thermodynamics, using two main approaches: one based on entropy and the other on ergotropy. First, we introduce a generalized approach to quantify non-Markovianity through the breakdown of monotonicity in thermodynamic functions. In this context, the entropy-based heat flow serves as a practical tool to witness and measure quantum memory in unital maps that do not reverse the sign of the internal energy. Next, we analyze the dynamics of ergotropy in open qubits under both Markovian and non-Markovian evolutions. We identify phenomena such as freezing and sudden death of ergotropy, and we establish an analytical relation between the change in ergotropy and the environment-induced work . This provides a clear physical interpretation for the additional term in the first law in the entropy-based formulation. Finally, we propose an ergotropy-based thermodynamic formulation, in which heat is reinterpreted in terms of the change of the passive state associated with the density operator governing the quantum dynamics. This approach allows one to measure non-Markovianity of unital maps more generally and accurately than the entropy-based heat flow. This advantage comes from the direct link between heat and von Neumann entropy, a property ensured by invariance under passive transformations. Moreover, the out-of-equilibrium temperature naturally remains non-negative, similarly to equilibrium thermodynamics.
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.
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.