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Exact Relation Between Coherence Decay and Entropy Production in a Dephasing

Humberto Arrabal

Published Apr 21, 2026• 0 citations
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Abstract

We derive an exact relation between quantum coherence decay and von Neumann entropy productionfor a qubit undergoing Markovian pure dephasing. For a general initial state with fixedpopulations, the entropy production rate is expressed in closed form in terms of the instantaneouscoherence and Bloch radius. In the equal-population case, the expression reduces to a coherenceonlylaw. The result provides a direct analytical connection between coherence loss and entropygeneration in open two-level systems.

DOI
10.6084/m9.figshare.32061003

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We derive an exact relation between quantum coherence decay and von Neumann entropy productionfor a qubit undergoing Markovian pure dephasing. For a general initial state with fixedpopulations, the entropy production rate is expressed in closed form in terms of the instantaneouscoherence and Bloch radius. In the equal-population case, the expression reduces to a coherenceonlylaw. The result provides a direct analytical connection between coherence loss and entropygeneration in open two-level systems.
We derive a closed-form relation between the von Neumann entropy rate and the coherence dynamicsof a qubit undergoing pure dephasing without assuming Markovianity. For fixed populations,the entropy rate is expressed solely in terms of the ℓ1-coherence and its time derivative. The Markovianexponential decay is recovered as a limiting case. In non-Markovian regimes, the relationpredicts intervals of negative entropy production associated with coherence revivals. In realisticquantum devices, deviations from the ideal relation provide a direct diagnostic of non-ideal dephasing,enabling detection and mitigation of noise and relaxation effects from coherence measurementsalone.
We derive an analytical relation between the von Neumann entropy rate and the coherence dynamicsof a qubit undergoing pure dephasing without assuming Markovianity. The result expresses˙S(t) solely in terms of the ℓ1-coherence C(t) and its time derivative ˙C (t), for fixed populations. TheMarkovian exponential decay is recovered as a special case. In non-Markovian regimes, the formulapredicts intervals of negative entropy rate associated with coherence revivals, providing a compactlink between information backflow and entropy dynamics.
We establish a direct connection between entropy production induced by quantum coherencedecay and fundamental limits on quantum computation rates. For a qubit undergoing Markovianpure dephasing, we derive an exact nonlinear relation between coherence decay and von Neumannentropy production, expressed in closed form through the Bloch radius. Combining this result withcoherence-constrained quantum speed limits, we show that entropy generation governs the effectivecoherence time and thereby constrains the maximum computational rate. Our results provide aunified thermodynamic and dynamical framework linking decoherence, irreversibility, and quantumspeed limits.
We establish a direct connection between entropy production induced by quantum coherencedecay and fundamental limits on quantum computation rates. For a qubit undergoing Markovianpure dephasing, we derive an exact nonlinear relation between coherence decay and von Neumannentropy production, expressed in closed form through the Bloch radius. Combining this result withcoherence-constrained quantum speed limits, we show that entropy generation governs the effectivecoherence time and thereby constrains the maximum computational rate. Our results provide aunified thermodynamic and dynamical framework linking decoherence, irreversibility, and quantumspeed limits.
We consider a single qubit undergoing pure dephasing with fixed populations and show that, fora natural pair of phase-opposite states, the trace distance coincides exactly with the ℓ1-norm ofcoherence. This allows the Breuer–Laine–Piilo (BLP) non-Markovianity indicator to be expresseddirectly in terms of single-qubit coherence dynamics within this setting, avoiding the usual optimizationover initial states. We also derive a simple relation between the entropy rate and coherence,showing that coherence revivals necessarily correspond to intervals of decreasing von Neumann entropy.Together, these results provide a transparent way to connect coherence, distinguishability,and information flow in dephasing qubits.
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.