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arXiv:2506.02268 · Physical review. E

Energetics of self-organization in a dissipative two-qubit system driven by single-photon pulses

Thiago Ganascini, W. Silva, D. Valente

Published Nov 6, 2025• 1 citation
arXivHTMLPDF

Abstract

Finding principles of nonequilibrium self-organization in dissipative quantum systems is an open problem. One example is the notion of quantum dissipative adaptation (QDA), that relates the transition probability between the ground states of a quantum system to the nonequilibrium work absorbed during the transition. However, QDA was originally derived with three-level systems in lambda (Λ) configuration. Here, we consider a two-qubit model driven by single-photon pulses. We find that the absorbed work is generally related to the sum of Λ-type transition probabilities, instead of the direct transition probability between the two ground states. Although this is equivalent to standard QDA in most scenarios, we find an exception whereby optimal self-organization is not accompanied by maximum work consumption. We show how quantum coherence leaves this kind of imprint in the energetics of self-organization in the present model.

DOI
10.1103/p8rm-l61j

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Finding principles of nonequilibrium self-organization in dissipative quantum systems is an open problem. One example is the notion of quantum dissipative adaptation (QDA), that relates the transition probability between the ground states of a quantum system to the nonequilibrium work absorbed during the transition. However, QDA was originally derived with three-level systems in lambda (Λ) configuration. Here, we consider a two-qubit model driven by single-photon pulses. We find that the absorbed work is generally related to the sum of Λ-type transition probabilities, instead of the direct transition probability between the two ground states. Although this is equivalent to standard QDA in most scenarios, we find an exception whereby optimal self-organization is not accompanied by maximum work consumption. We show how quantum coherence leaves this kind of imprint in the energetics of self-organization in the present model.
Classical dissipative adaptation is a hypothetical non-equilibrium thermodynamic principle of self-organization in driven matter, and it relates transition probabilities with the non-equilibrium work performed by an external drive on dissipative matter. Recently, the dissipative adaptation hypothesis was extended to a quantum regime with a theoretical model where only one single-photon pulse drives each atom of an ensemble. Here, we further generalize that quantum model by analytically showing that N cascaded single-photon pulses driving each atom still fulfill a quantum dissipative adaptation. Interestingly, we find that the level of self-organization achieved with two pulses can be matched with a single effective pulse only up to a threshold, above which the presence of more photons provides unparalleled degrees of self-organization.
Abstract Dissipative adaptation is a general thermodynamic mechanism that explains self-organization in a broad class of driven classical many-body systems. It establishes how the most likely (adapted) states of a system subjected to a given drive tend to be those following trajectories of highest work absorption, followed by dissipated heat to the reservoir. Here, we extend the dissipative adaptation phenomenon to the quantum realm. We employ a fully-quantized exactly solvable model, where the source of work on a three-level system is a single-photon pulse added to a zero-temperature infinite environment, a scenario that cannot be treated by the classical framework. We find a set of equalities relating adaptation likelihood, absorbed work, heat dissipation and variation of the informational entropy of the environment. Our proof of principle provides the starting point towards a quantum thermodynamics of driven self-organization.
We investigate the dissipative adaptation hypothesis in a quantum regime using a system-reservoir approach. This hypothesis proposes that self-organization arises from a system's ability to dissipate the work transiently absorbed from an external drive. We analyze the quantum dynamics of a driven open system described by a time-dependent spin-boson Hamiltonian modeling a particle in a metastable double-well potential with controllable asymmetry. We explore how the work provided by the dynamic potential is related to the transition probability between the two ground states of the double well. These studies motivate further investigations of the driven spin-boson model toward an understanding of the system's evolution and its thermodynamic implications.
The study of dissipative systems holds significant interest in physics.This thesis aims to explore these phenomena in both classical and quantum regimes.In the first part, we utilize the system-reservoir approach to investigate the dynamics of two Brownian particles immersed in the same bath.Two methods are employed to address this problem: one with bilinear coupling and the other with nonlinear coupling between the particles and the bath.The extension of the system to include two particles with bilinear coupling yields unphysical results, such as free-particle motion for the relative coordinate and a lack of interaction between closely spaced particles.To address this issue, authors have been introduced an exponential coupling.In this work, we propose a method to reconcile both linear and nonlinear couplings.We demonstrate how to derive the same nonlinear dissipation rates starting from the bilinear Lagrangian, achieved through a modified spectral function that explicitly depends on the distance between the particles.Additionally, we implement a modified spectral function to mitigate anomalous diffusion observed in the standard nonlinear model, along with a phenomenological model describing hydrodynamic interaction between a pair of Brownian particles in a viscous fluid.In the quantum regime, we adopt the same system-reservoir approach to investigate the dissipative adaptation hypothesis proposed by Jeremy England.This hypothesis proposes a general thermodynamic mechanism that explains the self-organization of systems through the dissipation of work absorbed from an external drive.In the second part of this thesis, we explore the quantum dynamics of systems subjected to an external drive, evaluating the thermodynamic quantities of a self-organization process.To do so, we utilize a time-dependent spin-boson Hamiltonian that characterizes a particle subject to a metastable double potential with time-dependent parameters controlling the asymmetry of the wells.Our objective is to demonstrate that the asymmetric potential can localize the particle in the unstable side of the well and verify that this transition results in the highest energy absorption.In conclusion, we propose further investigations into the driven spin-boson model to establish a comprehensive theory of the system's evolution and its thermodynamic implications.
Abstract The interplay of coherence and decoherence is played out in a three-level quantum system, in which the third level is incoherently coupled to the second one which itself is in coherent interaction with the first level. The study is based on a stochastic scenario in which the coherent, unitary evolution of the system is randomly interrupted by a Poisson-driven pulse sequence. In the absence of an external pulse, the system undergoes coherent, unitary evolution restricted to the subspace spanned by the first level (level 1) and the second level (level 2). The application of a pulse induces transitions between the second and the third level (level 3), thereby introducing non-unitary effects that perturb the otherwise isolated two-level dynamics. The pulses are assumed to have infinitesimal duration, with strengths modeled as random variables that are uncorrelated across different pulses. A representative model for the stochastically-averaged transition (super)operator mimicking the dynamics induced by the application of pulses allows for an analytical derivation of the matrix elements of the averaged density operator, especially, the element pertaining to the first level. When the system is initially in level 1, we obtain in particular the temporal behavior of the stay-put probability, that is, the probability P 1 ( t ) that the system is still in level 1 at time t. As a function of time, the quantity P 1 ( t ) exhibits a coherence-to-decoherence crossover behavior. At short times t ≪ 1 / λ , where λ is the average frequency at which pulses are applied to the system, coherent dynamics dominate. Consequently, P 1 ( t ) displays pronounced Rabi-like oscillations. At long times t ≫ 1 / λ , decoherence effects prevail, leading to an exponential decay of the form P 1 ( t ) − 1 / 3 ∼ exp ⁡ ( − λ t ) . The results are relevant in the context of well-established Rabi oscillations, applicable to molecular beams and magnetic resonance experiments, as well as in more contemporary frameworks including quantum information processing, quantum resetting protocols, and the theory of quantum trajectories.