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.
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.
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.
We analyze the heat exchange distribution of open quantum systems undergoing a thermal relaxation process with a time-dependent effective temperature. We show that such processes arise, for example, if the dynamics maximizes the entropy production. Using a two-point measurement scheme, we find an expression for the heat moment generating function that depends solely on the system's partition function and on the thermalization function (i.e., the law of cooling) describing the effective temperature. Applications include the relaxation of free bosonic and fermionic modes, for which closed-form expressions for the time-dependent heat distribution function are derived. Multiple free modes with arbitrary dispersion relations are also briefly discussed. In the semiclassical limit our formula agrees with previous results of the literature for the heat distribution of an optically trapped nanoscopic particle far from equilibrium.
The asymmetry between heating and cooling in open quantum systems is a hallmark of nonequilibrium dynamics, yet its thermodynamic origin has remained unclear. Here, we investigate the thermalization of a quantum system weakly coupled to a thermal bath, focusing on the entropy production rate and the quantum thermokinetic uncertainty relation (TKUR). We derive an analytical expression for the entropy production rate, showing that heating begins with a higher entropy production, which drives faster thermalization than cooling. The quantum TKUR links this asymmetry to heat-current fluctuations, demonstrating that larger entropy production suppresses fluctuations, making heating more stable than cooling. Our results reveal the thermodynamic basis of asymmetric thermalization and highlight uncertainty relations as key to nonequilibrium quantum dynamics.
A central open question in quantum thermodynamics is the identification of thermodynamic entropy away from equilibrium. Although thermodynamic entropy coincides with the von Neumann entropy for a Gibbs state at equilibrium, the thermodynamic role of quantum coherence generated during nonequilibrium evolution remains unclear. Here, we show that von Neumann entropy does not, in general, represent the thermodynamic entropy governing heat exchange in coherent nonequilibrium quantum systems. By integrating the resource theory of quantum coherence with thermodynamic principles, we develop a general framework for nonequilibrium quantum thermodynamics. We identify thermodynamic entropy with the energy entropy derived from energy-measurement statistics and introduce a dynamical temperature extending the equilibrium concept to nonequilibrium states. Consequently, we obtain an exact entropy-balance relation separating the entropy flux associated with heat exchange from the coherence-loss contribution to entropy production, establishing an operational connection between quantum coherence, heat flow, and total entropy change. Unlike approaches relying on equilibrium reference states or stationary Gibbs ensembles, our framework uses instantaneous dynamical quantities and remains valid throughout transient nonequilibrium evolution. It provides consistent dynamical definitions of temperature, work, heat, and free energy. Applying the formalism to an exactly solvable open quantum system, we show that the first and second laws hold throughout transient evolution and that equilibrium thermodynamics emerges dynamically in the weak-coupling long-time limit. Our results establish a unified framework for coherent nonequilibrium quantum thermodynamics and suggest opportunities for controlling heat dissipation through coherence engineering in quantum thermal technologies.
A model computational quantum thermodynamic network is constructed with two variable temperature baths coupled by a linker system, with an asymmetry in the coupling of the linker to the two baths. It is found in computational simulations that the baths come to "thermal equilibrium" at different bath energies and temperatures. In a sense, heat is observed to flow from cold to hot. A description is given in which a recently defined quantum entropy S_{univ}^{Q} for a pure state "universe" continues to increase after passing through the classical equilibrium point of equal temperatures, reaching a maximum at the asymmetric equilibrium. Thus, a second law account ΔS_{univ}^{Q}≥0 holds for the asymmetric quantum process. In contrast, a von Neumann entropy description fails to uphold the entropy law, with a maximum near when the two temperatures are equal, then a decrease ΔS^{vN}<0 on the way to the asymmetric equilibrium.
Abstract The theory of open quantum systems plays a fundamental role in several scientific and technological disciplines, from quantum computing and information science to molecular electronics and quantum thermodynamics. Despite its widespread relevance, a rigorous formulation of quantum dissipation in conjunction with thermal noise remains a topic of active research. In this work, we establish a formal correspondence between classical stochastic thermodynamics, in particular the Fokker–Planck and Klein–Kramers equations, and the quantum master equation. Building on prior studies of multiplicative noise in classical stochastic differential equations, we demonstrate that thermal noise at the quantum level manifests as a multidimensional geometric stochastic process. By applying canonical quantization, we introduce a novel Hermitian dissipation operator that serves as a quantum analogue of classical viscous friction. This operator allows for a well-defined expression of heat exchange between a system and its environment, enabling the formulation of an alternative quantum equipartition theorem. Our framework ensures a precise energy balance that aligns with the first law of thermodynamics and an entropy balance consistent with the second law. The theoretical formalism is applied to two prototypical quantum systems, the harmonic oscillator and a particle in an infinite potential well, for which it provides new insights into nonequilibrium thermodynamics at the quantum scale. Our results advance the understanding of dissipation in quantum systems and establish a foundation for future studies on stochastic thermodynamics in the quantum domain.