Trade-off between coherence and heat in a non-Markovian dephasing dynamics

Abstract

How quantum coherence influences thermodynamic behavior remains an open question in quantum thermodynamics. Here we investigate this relation within the pure dephasing framework, where a central qubit interacts with a finite Ising-like spin environment. Although the system's internal energy remains constant, the interaction induces decoherence and gives rise to nontrivial thermodynamic features. Within the two-point measurement approach, we show that the heat dissipated into the environment matches the coherent energy contribution appearing in a reformulated first law of quantum thermodynamics. Numerical calculations reveal oscillatory coherence dynamics, with revivals associated with information backflow and non-Markovian effects, as quantified by the Breuer-Laine-Piilo measure. We find that heat and coherence exhibit intertwined temporal behavior, with enhanced heat dissipation during coherence decay and reduced heat during revivals. These results suggest a connection between coherence dynamics and thermodynamic quantities in finite, closed composite systems undergoing pure dephasing.

Figures (5)

• Figure 1: (Color online) Schematic representation of a central qubit (blue sphere) interacting with an environment composed of $N$ spin-$1/2$ particles (black spheres) arranged in a ring geometry. The red halo indicates that the environment is initially prepared in a thermal equilibrium state at inverse temperature $\beta = T^{-1}$. The bath spins interact via a nearest-neighbor Ising coupling of strength $J_z$, and each spin is subject to a local magnetic field $h_z$. The qubit–environment interaction is characterized by the coupling constant $g$.
• Figure 2: (Color online) Time evolution of the $l_1$-norm of coherence for a qubit coupled to an Ising-like chain in a ring configuration with $g = 0.5\,|J_z|$ for different environment sizes $N = 3, 5, 7$. The oscillatory behavior indicates reversible information exchange between the qubit and the finite spin environment.
• Figure 3: (Color online) Time evolution of the $l_1$-norm of coherence for a qubit coupled to an Ising-like ring environment with fixed size $N = 7$, for different coupling strengths $g = 0.1\,|J_z|$, $0.3\,|J_z|$, and $0.5\,|J_z|$. Increasing $g$ enhances the system–environment interaction, leading to stronger decoherence.
• Figure 4: (Color online) Time evolution of the $l_1$-norm of coherence (solid line) and the information flow $\sigma_S(t)$ (dashed line) for $N=7$ and $g=0.5\,|J_z|$. Intervals where $\sigma_S(t)$ is positive coincide with coherence revivals, signaling non-Markovian behavior. The periodic alternation between decay and revival reflects the finite memory capacity of the spin environment.
• Figure 5: (Color online) Comparison between the time evolution of the mean heat $\langle Q \rangle$ (solid line) and the $l_1$-norm of coherence (dashed line) for $N=7$ and $g=0.5\,|J_z|$. Each maximum of $\langle Q \rangle$ coincides with a minimum of $|\Gamma(t)|$, indicating that heat dissipation occurs during decoherence.