我們提出了一種適用於任意耦合強度的量子熱力學重整化理論，該理論基於開放系統的精確主方程。與熱庫交換物質、能量和資訊的熱力學系統可以被建模為開放系統，並以廣義的 Fano-Anderson 哈密頓量來描述。我們發現，這些系統的約化密度矩陣的精確解在穩態極限下會趨向於吉布斯類型的狀態，這一結果與初始狀態及耦合強度無關。隨著耦合變強，系統哈密頓量、溫度和化學勢被重整化。其重整化效應是通過精確且非微擾的路徑積分得到的。只有使用這些重整化後的量，系統的穩態才能被表示為標準的吉布斯態。

該重整化能級的粒子數因此遵循玻色-愛因斯坦分佈（於玻色系統）和費米-狄拉克分佈（於費米系統），且以重整化物理量表示的熱力學公式和其物理保持不變。在弱耦合極限下，重整化的哈密頓量及溫度回到系統的原始哈密頓量和熱庫的初始溫度。由此，常規的統計力學和熱力學可以由求解量子力學嚴格地得到。在涉及多個不同環境的情況下，系統將達到一個最終溫度和化學勢。一般情況下，這些值可以與各個環境的初始溫度和化學勢不同。這證明了即使在弱耦合系統，重整化量子熱力學的必要性。

另一方面，我們研究了非平衡的強耦合量子熱力學，特別是瞬態的熱功轉換。我們發現，系統的耗散和漲落動力學引起了一個具有顯著非馬可夫效應的瞬態熱流。此外，能量和驅動場的重整化產生了量子功。在共振時，當腔體與自旋集群強耦合時，驅動場引起的功率可以顯著增強。我們的結果表明，非馬可夫效應加速了熱與功之間的能量轉換。

We develop a renormalization theory for quantum thermodynamics applicable to arbitrary coupling strengths, based on exact master equations for open systems. A thermodynamic system exchanging matter, energy, and information with its reservoirs can be modeled as an open system described by generalized Fano-Anderson Hamiltonians. We find that the exact solution for the density matrix of these systems approaches a Gibbs-type state in the steady-state limit, independent of the initial state and coupling strengths. As the couplings become strong, the system Hamiltonian, temperature, and chemical potential are renormalized, with nonperturbative effects obtained by exactly tracing over all reservoir states using coherent state path integrals. Only with these renormalized quantities can the exact steady state of the system be expressed as the standard Gibbs state.

Consequently, the exact steady-state particle occupations in the renormalized system's energy levels follow Bose-Einstein and Fermi-Dirac distributions for bosonic and fermionic systems, respectively. Thermodynamic formulas and physical interpretations are preserved in terms of renormalized quantities. In the weak-coupling limit, the renormalized Hamiltonian and temperature reduce to the system's bare Hamiltonian and the reservoir's initial temperature, ensuring that conventional statistical mechanics and thermodynamics are rigorously recovered from quantum dynamical evolution. In cases with multiple distinct environments, the system reaches a final temperature and chemical potential that differ from those of the individual environments. This illustrates the necessity of renormalization in quantum thermodynamics, even in the weak-coupling regimes.

On the other hand, we investigate the strong-coupling quantum thermodynamics of a hybrid quantum system far from equilibrium, focusing particularly on transient heat-work conversion. We find that the system's dissipation and fluctuation dynamics induce a transient quantum heat current with significant non-Markovian effects. Additionally, the renormalization of energy and the driving field generates quantum work power. Notably, non-Markovian dynamics can significantly enhance the driving-induced work power, especially when the cavity strongly couples to the spin ensemble at resonance. Our results demonstrate that non-Markovian effects enhance the conversion between heat and work.

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