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arXiv:2301.00196

Quantum coherence can be transformed into heat

Xue‐Qun Yan, Yan-Jiao Du, Hou, Wen-Tao, Xiaoming Liu

Published Dec 31, 2022• 0 citations
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Abstract

The first law of thermodynamics restates the law of conservation of energy. It partitions the change in energy of a system into two pieces, heat and work. While there is no ambiguity to define heat and work in classical thermodynamics, their classification in the quantum regime is not that obvious. Thus, the first law of thermodynamics becomes problematic in the quantum regime. However, recent studies have shown if contribution of quantum coherence is considered to the change of internal energy of the system, the first law of thermodynamics can be extended to the quantum domain. Here we investigate the new version of first law of thermodynamics for some quantum transformations by using two-level atomic system under non-dissipative channel. In our work we achieve a novel result that quantum coherence can be transformed into heat, and the heat can dissipate into the environments.

DOI
10.48550/arxiv.2301.00196

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The first law of thermodynamics restates the law of conservation of energy. It partitions the change in energy of a system into two pieces, heat and work. While there is no ambiguity to define heat and work in classical thermodynamics, their classification in the quantum regime is not that obvious. Thus, the first law of thermodynamics becomes problematic in the quantum regime. However, recent studies have shown if contribution of quantum coherence is considered to the change of internal energy of the system, the first law of thermodynamics can be extended to the quantum domain. Here we investigate the new version of first law of thermodynamics for some quantum transformations by using two-level atomic system under non-dissipative channel. In our work we achieve a novel result that quantum coherence can be transformed into heat, and the heat can dissipate into the environments.
Abstract Underlying the classical thermodynamic principles are analogous microscopic laws, arising from the fundamental axioms of quantum mechanics. These define quantum thermodynamic variables such as quantum work and heat and characterize the possible transformations of open quantum systems. The foremost quantum thermodynamic law is a simple statement concerning the conservation of energy. Nevertheless, there exist ambiguity and disagreement regarding the precise partition of a quantum system’s energy change to work and heat. By treating quantum mechanics as a comprehensive theory, applicable to both the micro and macroscopic domains, and employing dynamical symmetries, we bridge the gaps between five popular thermodynamic approaches to the first law. These include both autonomous and semi-classical formulations, which define work in terms of an ensemble average, as well as the single shot paradigm, where work is defined as a deterministic quantity.
In quantum thermodynamics, the decomposition of energy exchanges into heat and work remains an open problem beyond weak-coupling and slow-driving regimes. Recent formulations have shown that quantum coherence introduces additional energy contributions whose thermodynamic interpretation is still under debate, raising fundamental questions about the structure of the quantum first law. In this work, we investigate this problem through a time-dependent perturbative framework applied to the first law of quantum thermodynamics. By expanding the thermodynamic quantities up to second order, we derive explicit perturbative corrections for work, heat, and coherence contributions. Our results show that the coherence term can be consistently decomposed into coherent heat and coherent work, demonstrating that quantum coherence does not require the introduction of an independent energetic contribution beyond heat and work. The formalism resolves inconsistencies associated with previous formulations of the quantum first law, including the interpretation of coherence contributions and their connection with entropy fluxes. At second order, the perturbative corrections become directly connected to transition rates governed by Fermi's golden rule, establishing a bridge between microscopic quantum transitions and macroscopic thermodynamic quantities. These results provide a physically transparent framework to investigate coherence-driven thermodynamic processes and offer new perspectives for the analysis of driven quantum systems and nonequilibrium quantum technologies.
One of the fundamental questions in the emerging field of quantum thermodynamics is the role played by coherence in energetic processes that occur at the quantum level. Here we address this issue by investigating two different quantum versions of the first law of thermodynamics, derived from the classical definitions of work and heat. By doing so, we find out that there exists a mathematical inconsistency between both scenarios. We further show that the energetic contribution of the dynamics of coherence is the key ingredient to establish the consistency. Some examples involving two-level atomic systems are discussed in order to illustrate our findings.
The second law of thermodynamics places a limitation into which states a system can evolve into. For systems in contact with a heat bath, it can be combined with the law of energy conservation, and it says that a system can only evolve into another if the free energy goes down. Recently, it's been shown that there are actually many second laws, and that it is only for large macroscopic systems that they all become equivalent to the ordinary one. These additional second laws also hold for quantum systems, and are, in fact, often more relevant in this regime. They place a restriction on how the probabilities of energy levels can evolve. Here, we consider additional restrictions on how the coherences between energy levels can evolve. Coherences can only go down, and we provide a set of restrictions which limit the extent to which they can be maintained. We find that coherences over energy levels must decay at rates that are suitably adapted to the transition rates between energy levels. We show that the limitations are matched in the case of a single qubit, in which case we obtain the full characterization of state-to-state transformations. For higher dimensions, we conjecture that more severe constraints exist. We also introduce a new class of thermodynamical operations which allow for greater manipulation of coherences and study its power with respect to a class of operations known as thermal operations.
Assigning the variations of internal energy into heat or work contributions is a challenging task due to the fact that these properties are trajectory dependent. A number of proposals have been put forward for open quantum systems following an arbitrary dynamics. We here focus on nonequilibrium thermodynamics of a two-level system and explore in addition to the conventional approach, two definitions motivated by either classical work or heat in which the driving Hamiltonian or the trajectory itself, respectively, are used to set up a reference basis. We first give the thermodynamic properties for an arbitrary dynamics and illustrate the results on the Bloch sphere. Then, we solve the particular example of a periodically driven qubit interacting with a dissipative and decoherence bath. Our results illustrate the trajectory-dependent character of heat and work and how contributions originally assigned to dissipation in the Lindblad equation can become a coherent part assigned to work.
The question of with what we associate work and heat in a quantum thermodynamic process has been extensively discussed, mostly for systems with time-dependent Hamiltonians. In this paper, we aim to investigate the energy exchanged between two quantum systems through interaction where the Hamiltonian of the system is time-independent. An entropy-based re-definitions of heat and work are presented for these quantum thermodynamic systems therefore an entropy-based formalism of both the first and the second laws of thermodynamics are introduced. We will use the genuine reasoning based on which Clausius originally defined work and heat. The change in the energy which is accompanied by a change in the entropy is identified as heat, while any change in the energy which does not lead to a change in the entropy is known as work. It will be seen that quantum coherence does not allow all the energy exchanged between two quantum systems to be only of the heat form. Several examples will also be discussed. Finally, we will examine irreversibility from our entropy-based formalism of quantum thermodynamics.