Based on the "Interface Projection Realism" framework, this paper rigorously derives the universal formula for internal dissipation power and the microscopic expression for the energy distribution ratio f from first principles. We treat the qubit (Q), the interfacial defect network (D), and the bulk dissipation channel (B) as a self-contained total system, no longer presupposing any part of it as an external environment. By applying the Born-Markov approximation to the degrees of freedom of D and B, we obtain the reduced master equation for Q, and subsequently calculate the net energy flow rate from Q to the incoherent degrees of freedom—the internal dissipation power R_internal. The result is: R_internal = ħω_q [Γ↓ ⟨n⟩ - Γ↑ (1-⟨n⟩)], where Γ↓ and Γ↑ are transition rates determined by the Q-D coupling and the internal structure of D, and ⟨n⟩ is the excited state population of Q. This formula does not rely on any thermal equilibrium assumptions and is applicable to arbitrary Markovian non-equilibrium steady states. Building on this, we define the total effective power absorbed by the system as R_total = ⟨∂H_drive/∂t⟩ and introduce the system's stored energy E_stored = ⟨H_Q⟩. Under periodic averaging, the energy conservation equation reads dE_stored/dt = R_total - R_internal, where the overline denotes time average. The energy distribution ratio f = R_internal / R_total satisfies f = 1 in the periodic steady state where dE_stored/dt = 0; during transients, f can deviate from 1, its specific expression depending on microscopic parameters, reflecting the degree of deviation from the steady state. We further demonstrate that when D and B are in thermal equilibrium, the above formula reduces to the traditional fluctuation-dissipation theorem. This paper proves that the universal formula for internal dissipation power naturally contains the fluctuation-dissipation theorem under thermal equilibrium conditions, while its validity in non-equilibrium states constitutes a non-equilibrium generalization of the traditional theorem, providing a unified theoretical foundation for understanding the energetic origin of quantum decoherence.
The theory of open quantum systems represents one of the major developments of quantum mechanics over the last 50 years. Its central object of study is constituted by quantum systems that cannot be regarded as fully isolated, but instead interact with additional degrees of freedom, giving rise to irreversible phenomena such as dissipation and decoherence. The tools provided by this framework are nowadays of paramount importance across many active areas of research, including quantum computation, thermodynamics, metrology and biology. In this thesis, we investigate three main topics within the field. The first contribution concerns the microscopic derivation of the evolution equations, socalled quantum master equations, for open systems which are also subject to external driving fields. Standard techniques developed for time-independent Hamiltonians encounter several difficulties in the time-dependent case, largely restricting their applicability to specific instances, such as periodic or adiabatic drivings. In contrast, a core result of the derivation presented in the thesis is that, when the environment is sufficiently Markovian (essentially, memoryless), the non-adiabatic contributions to the driving field can be neglected in a controlled fashion, yielding an accurate master equation with time-dependent generator, capable of correctly reproducing the open dynamics even for strong drivings. This result is further supported by benchmarks against numerically exact simulations. The second contribution addresses the long-time behavior of general types of (Markovian) quantum master equations, including those of the form introduced above. While this problem has been extensively analyzed in the time-independent setting, virtually no results are known for time-dependent generators. In particular, we establish the foundations of a general theory of relaxation, that is, convergence towards an asymptotic trajectory in the long-time limit, independently of the initial state. The main results include a theorem guaranteeing sufficient conditions for relaxation and the derivation of a rate function governing the convergence to the asymptotic trajectory. The analysis is further extended to a simple non-Markovian case. Moreover, we treat in detail the specific master equation derived in the first part, connecting the aforementioned relaxation property directly to the underlying microscopic dynamics. The third contribution investigates chirality-induced spin selectivity (CISS) effects from the perspective of open quantum systems. Although the majority of theoretical studies aiming to model CISS are based on a coherent description of the spin dynamics, such effects have been observed also for electrons subject to incoherent transport across molecular networks. In this regard, we provide a rigorous ab initio derivation of the microscopic Hamiltonian describing the electronic transport, incorporating electron spin effects and contributions stemming from the nuclear vibrations. Within this result, we critically revise a master equation approach aiming to explain the origin of CISS effects observed in photosynthetic complexes. Taken together, these contributions offer fresh insights and original results on the interplay between driving fields and dissipation, relaxation phenomena, and electronic spin transport in the presence of incoherent dynamics. More broadly, these results provide new theoretical tools with several potential applications in quantum technologies, from modeling of control pulses in noisy environments to quantum reservoir engineering, and contribute to a deeper understanding of the role of quantum effects in biological systems.
Important Update on March 9, 2026: In this version, the description of environmental effects has been corrected: they are now properly treated as encapsulated within the effective spectral density of the interfacial defect network D, rather than as direct driving terms. All core results and conclusions remain unchanged, but the physical interpretation is refined to align with the energy distribution framework introduced in Part II of this series. Version 2 This paper is the third in the "Interface-Projected Realism" series. This series of work aims to establish a new theoretical paradigm: Ontologically, replace probabilistic wave function descriptions with deterministic energy flow; Methodologically, redefine physical reality as an interactive whole composed of quantum units (
Q), an interfacial defect network (
D), and bulk channels (
B). In the first work, an exact relationship between energy flow and relaxation rate was established, providing a formal bridge for the paradigm shift. In the second work, the "Energy Distribution Framework" was proposed, demonstrating that dissipation is the deterministic allocation of energy between
Q and
D, and deriving the universal formula for internal dissipation power
Rint=ℏωq[Γ↓⟨n⟩−Γ↑(1−⟨n⟩)], where the relaxation rates are completely determined by the internal structure of
D, revealing the core role of the energy distribution ratio
f. This paper generalizes this new paradigm based on energy distribution from single-body to many-body systems. The core step is to define multiple
Q contacts and their shared
D and
B together as a new, unified composite system. Within this framework, the traditionally complex "many-body correlated dissipation" is clearly interpreted as a macroscopic result of the deterministic flow of energy within this composite system, governed by allocation and transport rules determined by the structure of the
D network. Through rigorous coarse-graining of this overall system, this paper derives the governing equation for the evolution of its internal energy density field
u(r,t)—a classical reaction-diffusion equation:
∂t∂u=Rtotal−γ0(r)u+∇⋅(γ2∇u).Here, the local dissipation rate
γ0(r) and the diffusion coefficient
γ2 are completely determined by the properties of the
D network, corresponding respectively to the spatial distribution of the energy distribution ratio
f from the second paper and the redistribution effect induced by its correlations. This theory is not only logically self-consistent but also provides a unified explanation for multiple cutting-edge experiments. This paper marks that a physical framework based on deterministic energy distribution and transport can now systematically describe many-body correlation phenomena, providing crucial support for the completeness of the new paradigm. \textbf{Keywords}: Interface-Projected Realism; Energy Distribution; Many-Body Systems; Correlated Dissipation; Reaction-Diffusion Equation Version 1 Traditional quantum theory typically attributes energy dissipation to random perturbations from the external environment. Based on the "Interfacial Projected Realism" framework, this work re-examines the nature of energy dissipation from a novel perspective, treating the qubit, the interfacial defect network, and the bulk dissipation channel as a self-contained total system. We first rigorously derive the universal formula for internal dissipation power and the energy distribution ratio
f in single-body quantum systems, and then extend these concepts to many-body systems. Starting from a microscopic Hamiltonian coupling multiple qubits to a common quantized field and employing the Nakajima-Zwanzig projection operator technique, we obtain a universal expression for the energy dissipated from a many-body system to the environment. Applying this result to the specific model of multiple two-level systems coupled to a common bosonic field yields a collective master equation where the dissipation coefficient matrix
Γij encodes all spatial and coupling information. Through systematic coarse-graining, gradient expansion, and semiclassical approximation, we derive for the first time from an energy-distribution perspective a closed set of macroscopic equations for the local system energy density
u(r,t) and the environmental field energy density
U(r,t):
∂t∂u=Rtotal(r,t)−γ0(U)u+∇⋅(γ2(U)∇u)∂t∂U=D∇2U−ΓBU+ρ(r)γ0(U)u Within this framework, the energy distribution ratio
f(r,t)=γ0u/Rtotal emerges naturally as a macroscopic quantity, its physical essence being jointly determined by the system’s microscopic coupling structure (embodied by
Γij) and quantum statistical state. The theory quantitatively explains several long-unexplained anomalous phenomena in cutting-edge experiments, demonstrates strong testability, and lays a solid foundation for exploring deeper connections between energy distribution and macroscopic physics. For the exact mathematical formulation and detailed derivations, please refer to the PDF file.
Update Notice (v2) 2026/2/13 This preprint has been superseded by a significantly revised version, which has been uploaded as a separate submission. In the original version (v1), the relation between internal dissipation power and the energy relaxation rate was introduced in a phenomenological manner. However, a rigorous first-principles derivation has now been completed in a companion paper [Guo (2026), Exact Relation between Internal Dissipation Power and Energy Relaxation Rate——A Rigorous Derivation in Markovian Quantum Systems]. Using this exact relation Rinternal=ℏωqΓ1⟨σ+σ−⟩Rinternal=ℏωqΓ1⟨σ+σ−⟩, the previously phenomenological "energy competition" framework has been reformulated from the ground up. As a result: The parameter ff (energy allocation fraction) is now rigorously defined in terms of experimentally accessible quantities, rather than introduced as a phenomenological fit parameter. The previous phenomenological arguments and associated experimental discussions in v1 are no longer valid and should be disregarded. The new version provides a complete microscopic foundation for the theory of energy competition in superconducting qubit decoherence. Readers are strongly encouraged to consult the latest version (available at [10.5281/zenodo.18624328) for a comprehensive and self-contained treatment. Version 2 The decoherence time of superconducting qubits is commonly believed to be dominatedby dielectric loss (loss tangent tan 𝛿). Multiple experimental studies have found an empiricalscaling relationship approximately Γ ∝ (tan 𝛿)0.7 between the decoherence rate Γ = 1/𝑇2and tan 𝛿. Based on the ”Interface Projection Realism” framework, this paper proposes apossible new physical picture for decoherence. By analyzing 25 superconducting quantumdevices covering single-qubit, multi-qubit, hybrid systems, and 3D integration, we observethe dispersion of this scaling relationship in optimized interface samples. Experimentaldata show that unoptimized samples indeed follow Γ ∝ (tan 𝛿)0.7, while optimized samplesexhibit significant dispersion in the scaling exponent.To explain this phenomenon, we propose a decoherence theoretical framework basedon the ”Energy Competition” picture. This framework reinterprets decoherence as the re-sult of competitive allocation of the input microwave energy between the ”internal dissipa-tion channel generating noise” and the ”net channel maintaining coherence.” This physicalpicture is a concrete implementation of Interface Projection Realism in the decoherenceproblem. By introducing the energy allocation ratio 𝑓 and the interface intrinsic competi-tion coefficient 𝜒, the theoretical framework predicts that the pure dephasing rate satisfiesΓ𝜙 = 𝜒 · 𝑓 /(1 − 𝑓 ) in the strong suppression limit. This framework provides a possibleexplanation for the dispersion of scaling behavior. Furthermore, the analysis of paired sam-ples (with the same tan 𝛿 but 𝑇2 differing by a factor of 16.7) provides indirect evidence forthe possibility of 𝑓 being an independent parameter.Moreover, the theoretical framework can unify the explanation of decoherence data fromsingle qubits to complex systems and proposes unique predictions that can be directly veri-fied experimentally, such as power independence and noise spectrum evolution. This workprovides a new perspective based on Interface Projection Realism for understanding quan-tum decoherence and deepens the goal of interface engineering from simply reducing lossto possibly regulating the energy allocation ratio 𝑓 . Important Update (Updated January 28, 2026) The square-root decoherence scaling law (Γ∝κeff) with scaling exponent α=0.5 reported in this work was derived via empirical fitting against superconducting qubit experimental datasets, based on the "resource competition theory at dynamic projection interfaces." This exponent was established under the framework of phenomenological analysis, leveraging established physical heuristics for intrinsic material loss and the loss angle tanδ, and exhibited high fitting goodness for low-noise, weak-coupling quantum systems. Subsequent research has advanced this framework to a comprehensive mathematical-physical theory—Interface Projection Realism (IPR)—grounded in quantum information first principles. A key innovation of IPR is the introduction of the transmissivity field Ξ(x,t) (as the fundamental order parameter describing the quantum-classical interface) and the rigorous derivation of its quantum information dynamics equation. By analyzing an expanded set of superconducting qubit decoherence data through weighted least-squares fitting (yielding R2=0.9987, an extremely significant F-statistic of 2856.3), the universal decoherence scaling exponent is refined to α=0.792±0.008. This revised exponent corresponds to a synergy index m=4.81±0.15, which originates from the cooperative effect of five major noise channels (dielectric loss, quasiparticle tunneling, flux noise, charge noise, and radiation loss) embedded in quantum channel dynamics. IPR further makes two independent testable predictions—equivalence principle violation (Δa/aˉ∼2.3×10−9) and a first-principles calculation of dark energy density (ρΛ≈4.2×10−47GeV4, consistent with Planck 2018 observations)—demonstrating its explanatory power across quantum decoherence, quantum gravity, and cosmology. A complete account of the theoretical derivation, microphysical mechanism, and experimental corroboration is provided in our latest work: Interface Projection Realism: A Multiscale Unified Theory Based on Quantum Information Dynamics (Zenodo, Version v3, DOI: 10.5281/zenodo.18400122, January 28, 2026). This preprint serves as a foundational stage-specific contribution to the evolutionary trajectory of the IPR framework. The α=0.5 square-root scaling relation remains a valid limiting case for low-noise, weak-coupling material systems, while the refined α=0.792 exponent offers a universal description across broader material and noise conditions. Version 1 We report a universal square-root scaling law between the decoherence rate Γ of a quantum system and its effective intrinsic dissipation κeff, i.e., Γ ∝ √ κeff. This empirical law, observed across platforms like superconducting qubits, finds its mechanistic explanation within a new theoretical framework of resource com petition at a dynamic projection interface. The framework posits that our (3+1)-dimensional classical spacetime emerges from a higher-dimensional realm of potentialities (L1) through a filtering process governed by the interface perme ability field Ξ(x, t). Finite information-energy flux from L1 is contested between systems’ tendency to maintain quantum coherence and their intrinsic demand to dissipate noise for classical stability, quantified by κeff. From this competition dy namics, we derive the square-root scaling law. The model further provides unified, objective descriptions of quantum measurement as channel locking and of grav ity as emergence from Ξ-field distortion. Several concrete, testable predictions are proposed, including nonlinear jumps in coherence at phase transitions and a novel testable correlation for equivalence principle experiments.
The interrelationship between the non-Markovian stochastic Schr\"odinger equations and the corresponding non-Markovian master equations is investigated in the finite-temperature regimes. We show that the general finite-temperature non-Markovian trajectories can be used to derive the corresponding non-Markovian master equations. A simple, yet important solvable example is the well-known damped harmonic oscillator model in which a harmonic oscillator is coupled to a finite-temperature reservoir in the rotating-wave approximation. The exact convolutionless master equation for the damped harmonic oscillator is obtained by averaging the quantum trajectories, relying upon no assumption of coupling strength or time scale. The master equation derived in this way automatically preserves the positivity, Hermiticity, and unity.
Deriving the laws of thermodynamics from an underlying microscopic picture is a central quest of statistical mechanics. The present article focuses on the derivation of the first and second law of thermodynamics for closed and open quantum systems, where such foundational questions in addition become practically relevant for emergent nanotechnologies. Recent progress is presented in a self-contained way, with an emphasis on general ideas and useful tools instead of particular applications. We identify limits and conceptual shortcomings of previous approaches. Then, we propose a novel, unifying perspective, which starts from a microscopic definition of nonequilibrium thermodynamic entropy. The change of this entropy is identified with the entropy production, which satisfies a fluctuation theorem for a large class of initial states. Moreover, this entropy production can be naturally separated into a quantum and a classical component. Within our framework, we introduce the notions of recoverable work and remaining heat. In the case of a weakly perturbed ideal thermal bath this approach is in quantitative agreement with previous ones, thus ensuring their thermodynamic consistency.