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Entropy Production as a Fundamental Constraint on Quantum Speed Limits via

Humberto Arrabal

Published Apr 21, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.6084/m9.figshare.32061438

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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 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.
In the framework of the recent quest for well-behaved nonlinear extensions of the traditional Schrödinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the microscopic level, a recent paper [Gheorghiu-Svirschevski 2001 Phys. Rev. A 63 054102] reproposes the nonlinear equation of motion proposed by the present author [see Beretta G P 1987 Found. Phys. 17 365 and references therein] for quantum (thermo)dynamics of a single isolated indivisible constituent system, such as a single particle, qubit, qudit, spin or atomic system, or a Bose-Einstein or Fermi-Dirac field. As already proved, such nonlinear dynamics entails a fundamental unifying microscopic proof and extension of Onsager's reciprocity and Callen's fluctuation-dissipation relations to all nonequilibrium states, close and far from thermodynamic equilibrium. In this paper we propose a brief but self-contained review of the main results already proved, including the explicit geometrical construction of the equation of motion from the steepest-entropy-ascent ansatz and its exact mathematical and conceptual equivalence with the maximal-entropy-generation variational-principle formulation presented in Gheorghiu-Svirschevski S 2001 Phys. Rev. A 63 022105. Moreover, we show how it can be extended to the case of a composite system to obtain the general form of the equation of motion, consistent with the demanding requirements of strong separability and of compatibility with general thermodynamics principles. The irreversible term in the equation of motion describes the spontaneous attraction of the state operator in the direction of steepest entropy ascent, thus implementing the maximum entropy production principle in quantum theory. The time rate at which the path of steepest entropy ascent is followed has so far been left unspecified. As a step towards the identification of such rate, here we propose a possible, well-behaved and intriguing, general closure of the dynamics, compatible with the nontrivial requirements of strong separability. Based on the time–energy Heisenberg uncertainty relation, we derive a lower bound to the internal-relaxation-time functionals that determine the rate of entropy generation. This bound entails an upper bound to the rate of entropy generation. By this extreme maximal-entropy-generation-rate ansatz, each indivisible subsystem follows the direction of steepest locally perceived entropy ascent at the highest rate compatible with the time– energy uncertainty principle.
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.
The study and control of coherence in quantum systems is one of the most exciting recent developments in physics. Quantum coherence plays a crucial role in emerging quantum technologies as well as fundamental experiments. A major obstacle to the utilization of quantum effects is decoherence, primarily in the form of dephasing that destroys quantum coherence, and leads to effective classical behavior. We show that there are universal relationships governing dephasing that constrain the relative rates at which quantum correlations can disappear. These lead effectively to speed limits which become especially important in multipartite systems.