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Heating-cooling asymmetry in quantum systems

Camila Raupp da Luz

Published Aug 26, 2026• 0 citations
Publisher

Abstract

Understanding how quantum systems equilibrate is a fundamental question with implications for quantum technologies, such as state preparation for quantum computing. However, linear response theory fails to explain the thermal relaxation of far-from-equilibrium classical and quantum systems. In this context, recent studies have reported a relaxation asymmetry, where heating is faster than cooling for initial states that are thermodynamically equidistant from equilibrium, but understanding how quantum resources affect this asymmetry is still an open question. In this work, we investigate the heating and cooling asymmetry in discrete and continuous-variable quantum systems. For the discrete case, we study two interacting qubits coupled to a global bosonic bath, focusing on the effects of initial coherences, steady state correlations generated by the dynamics and local non-Markovianity. For the continuous case, we consider Gaussian states and compare the thermal relaxation asymmetry of displaced and squeezed states. Our results for the discrete case indicate that non-Markovianity may accelerate thermal relaxation, while the initial coherences do not change the equilibration time. In Gaussian systems, applying the displacement operator in the initial states does not affect the asymmetry, but applying the squeezing operator reduces the asymmetry. Additionally, we show an invertion of the asymmetry, making cooling faster than heating, by squeezing the hotter state and displacing the cooler state.

DOI
10.11606/d.76.2026.tde-20102026-141121

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Understanding how quantum systems equilibrate is a fundamental question with implications for quantum technologies, such as state preparation for quantum computing. However, linear response theory fails to explain the thermal relaxation of far-from-equilibrium classical and quantum systems. In this context, recent studies have reported a relaxation asymmetry, where heating is faster than cooling for initial states that are thermodynamically equidistant from equilibrium, but understanding how quantum resources affect this asymmetry is still an open question. In this work, we investigate the heating and cooling asymmetry in discrete and continuous-variable quantum systems. For the discrete case, we study two interacting qubits coupled to a global bosonic bath, focusing on the effects of initial coherences, steady state correlations generated by the dynamics and local non-Markovianity. For the continuous case, we consider Gaussian states and compare the thermal relaxation asymmetry of displaced and squeezed states. Our results for the discrete case indicate that non-Markovianity may accelerate thermal relaxation, while the initial coherences do not change the equilibration time. In Gaussian systems, applying the displacement operator in the initial states does not affect the asymmetry, but applying the squeezing operator reduces the asymmetry. Additionally, we show an invertion of the asymmetry, making cooling faster than heating, by squeezing the hotter state and displacing the cooler state.
An intriguing phenomenon in nonequilibrium quantum thermodynamics is the asymmetry of thermal processes. Relaxation to thermal equilibrium is the most important dissipative process, being a key concept for the design of heat engines and refrigerators, contributing to the study of foundational questions of thermodynamics, and being relevant for quantum computing through the process of algorithmic cooling. Despite their importance, the dynamics of these processes are far from being understood. We show that the free relaxation to thermal equilibrium follows intrinsically different paths depending on whether it involves the temperature of the system to increase or to decrease. Our theory is exemplified using the recently developed thermal kinematics based on information geometry theory, utilizing three prototypical examples: a two-level system, the quantum harmonic oscillator, and a trapped quantum Brownian particle, in all cases showing faster heating than cooling under the appropriate conditions. A general understanding is obtained based on the spectral decomposition of the Liouvillian and the spectral gap of reciprocal processes.
Cooling quantum systems with finite resources is a central task in quantum technologies and has been extensively explored in discrete-variable settings. As continuous-variable (CV) platforms play an increasingly important role in quantum information processing, it becomes crucial to understand the fundamental limitations of cooling bosonic systems. In this work, we develop a general framework for cooling CV systems, identifying both the constraints imposed by Gaussianity and the advantages enabled by non-Gaussian interactions. We derive a reachable bound on the cooling performance of Gaussian operations that applies to arbitrary cooling architectures. By optimizing over all protocols saturating this bound, we further identify the most efficient scheme, which minimizes dissipated energy for a given number of ancilla modes. Beyond Gaussian operations, we show that ppp-excitation exchange exploits non-Gaussian resources to achieve a ppp-fold enhancement of the cooling limit. Our results establish the fundamental limits of CV heat-bath algorithmic cooling and reveal the crucial role of non-Gaussianity in surpassing Gaussian cooling barriers.
The study of thermal operations allows one to investigate the ultimate possibilities of quantum states and of nanoscale thermal machines. Whilst fairly general, these results typically do not apply to continuous variable systems and do not take into account that, in many practically relevant settings, system-environment interactions are effectively bilinear. Here we tackle these issues by focusing on Gaussian quantum states and channels. We provide a complete characterization of the most general Gaussian thermal operation acting on an arbitrary number of bosonic modes, which turn out to be all embeddable in a Markovian dynamics, and derive necessary and sufficient conditions for state transformations under such operations in the single-mode case, encompassing states with nonzero coherence in the energy eigenbasis (i.e., squeezed states). Our analysis leads to a no-go result for the technologically relevant task of algorithmic cooling: We show that it is impossible to reduce the entropy of a system coupled to a Gaussian environment below its own or the environmental temperature, by means of a sequence of Gaussian thermal operations interspersed by arbitrary (even non-Gaussian) unitaries. These findings establish fundamental constraints on the usefulness of Gaussian resources for quantum thermodynamic processes.
This thesis investigates the quantum Mpemba effect, where an initially hotter system cools down faster than an initially colder one. This was demonstrated in a qubit system coupled to two environments. A thermal state is chosen as the initial state and then left to freely equilibrate. It was shown that the initial thermal state can be chosen in a way to accelerate the resulting relaxation process. The Liouvillian dynamics were analyzed and, by eliminating the contribution of the slowest decaying eigenmode (SDM) corresponding to accelerated relaxation dynamics, the effect was demonstrated. All states with vanishing SDM contributions were considered and found to belong to a plane in the Bloch sphere corresponding to a reduced state space. A thermal state could be shown to exist in this subspace, which is the Mpemba state that relaxes the fastest. The numerical relaxation dynamics were computed and the accelerated behavior of the Mpemba state verified. The fidelity of the Mpemba state also exhibits a steeper decay, consistent with the faster-decaying modes. The results were found to only strongly affect the solution in regions close to the steady state.
The challenge of harnessing entanglement during the non-equilibrium dynamics of open quantum systems, especially at high temperatures, is highly prominent within recent scientific researches. Due to the ongoing trend of miniaturization of quantum devices that exploit quantum correlations, proposing novel schemes to overcome this challenge is itself a crucial task within current quantum technological research. We contribute to this research by proposing a new scheme to control entanglement dynamics of a non-equilibrium two-qubit Heisenberg XXZ spin chain model in an external magnetic field. The design of the scheme is based on a coupling asymmetry in the model induced by the asymmetrical connection of qubits to two independent thermal reservoirs. While in the absence of the coupling asymmetry, non-equilibrium effects generally suppress the dynamical generation of thermal entanglement, making entanglement production impossible at high mean temperatures of reservoirs, it is shown that this asymmetry in the coupling potentially enables us to generate a maximal non-equilibrium entanglement even in the high mean temperature regime. We show that the coupling asymmetry can also lead to a complete protection of the maximum initial entanglement between the qubits at high mean temperatures of the reservoirs thanks to the non-equilibrium conditions. Depending on the initial state of the two qubits, this can be achieved either by accessing a coherence-free subspace or by fully reviving the initial qubit-qubit entanglement. Furthermore, we investigate the quantum heat transport of the chain, and find that by turning on the asymmetry in the qubit-reservoir coupling, although the chain loses its initial thermal rectification property over time, it regains this property and maintain it until the non-equilibrium steady state is reached. Our results show that, at higher temperature gradients, the chain leverages the steady-state entanglement to completely block the heat released from the hot reservoir. Our findings can be significant for heat management in quantum computing devices such as solid-state thermal circuits.
Since its rediscovery in the twentieth century, the Mpemba effect, where a far-from-equilibrium state may relax faster than a state closer to equilibrium, has been extensively studied in classical systems and has recently received attention in quantum systems. Many theories explaining this counter-intuitive behavior in classical systems rely on memory effects. However, in quantum systems, the relation between the Mpemba effect and memory has remained unexplored. In this Letter, we consider general non-Markovian open quantum systems and reveal new classes of quantum Mpemba effects, with no analog in Markovian quantum dynamics. Generically, open quantum dynamics possess a finite memory time and a unique steady state. Because of non-Markovian dynamics, even if the system is initialized in the steady state it can take a long time to relax back. We find other initial states that reach the steady state much faster. Most notably, we demonstrate that there can be an initial state in which the system reaches the steady state within the finite memory time itself, giving the fastest possible relaxation to stationarity. We verify the effect for quantum dot systems coupled to electronic reservoirs in equilibrium and nonequilibrium setups at weak, intermediate and strong coupling. Our Letter provides new insights into the rich physics underlying accelerated relaxation in quantum systems.