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Entropy

Can Quantum Correlations Lead to Violation of the Second Law of Thermodynamics?

Alexey V. Melkikh

Published May 7, 2021• 4 citations
Publisher

Abstract

Quantum entanglement can cause the efficiency of a heat engine to be greater than the efficiency of the Carnot cycle. However, this does not mean a violation of the second law of thermodynamics, since there is no local equilibrium for pure quantum states, and, in the absence of local equilibrium, thermodynamics cannot be formulated correctly. Von Neumann entropy is not a thermodynamic quantity, although it can characterize the ordering of a system. In the case of the entanglement of the particles of the system with the environment, the concept of an isolated system should be refined. In any case, quantum correlations cannot lead to a violation of the second law of thermodynamics in any of its formulations. This article is devoted to a technical discussion of the expected results on the role of quantum entanglement in thermodynamics.

DOI
10.3390/e23050573

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Quantum entanglement can cause the efficiency of a heat engine to be greater than the efficiency of the Carnot cycle. However, this does not mean a violation of the second law of thermodynamics, since there is no local equilibrium for pure quantum states, and, in the absence of local equilibrium, thermodynamics cannot be formulated correctly. Von Neumann entropy is not a thermodynamic quantity, although it can characterize the ordering of a system. In the case of the entanglement of the particles of the system with the environment, the concept of an isolated system should be refined. In any case, quantum correlations cannot lead to a violation of the second law of thermodynamics in any of its formulations. This article is devoted to a technical discussion of the expected results on the role of quantum entanglement in thermodynamics.
The second law of thermodynamics has been proven by many facts in classical world. Is there any new property of it in quantum world? In this paper, we calculate the change of entropy in T.D. Kieu's model for quantum heat engine (QHE) and prove the broad validity of the second law of thermodynamics. It is shown that the entropy of the quantum heat engine neither decreases in a whole cycle, nor decreases in either stage of the cycle. The second law of thermodynamics still holds in this QHE model. Moreover, although the modified quantum heat engine is capable of extracting more work, its efficiency does not improve at all. It is neither beyond the efficiency of T.D. Kieu's initial model, nor greater than the reversible Carnot efficiency.
The Carnot statement of the second law of thermodynamics poses an upper limit on the efficiency of all heat engines. Recently, it has been studied whether generic quantum features such as coherence and quantum entanglement could allow for quantum devices with efficiencies larger than the Carnot efficiency. The present study shows that this is not permitted by the laws of thermodynamics-independent of the model. We will show that rather the definition of heat has to be modified to account for the thermodynamic cost of maintaining non-Gibbsian equilibrium states. Our theoretical findings are illustrated for two experimentally relevant examples.
A heat engine undergoes a cyclic operation while in equilibrium with the net result of conversion of heat into work. Quantum effects such as superposition of states can improve an engine's efficiency by breaking detailed balance, but this improvement comes at a cost due to excess entropy generated from collapse of superpositions on measurement. We quantify these competing facets for a quantum ratchet composed of an ensemble of pairs of interacting two-level atoms. We suggest that the measurement postulate of quantum mechanics is intricately connected to the second law of thermodynamics. More precisely, if quantum collapse is not inherently random, then the second law of thermodynamics can be violated. Our results challenge the conventional approach of simply quantifying quantum correlations as a thermodynamic work deficit.
Recent theoretical and experimental work on the foundations of statistical mechanics and thermodynamics has shown that quantum pure states typically evolve to thermal equilibrium. We focus on formulating the second law of thermodynamics for these states. The standard quantum von Neumann quantum entropy is constant during equilibration, S^{vN}=0, in apparent conflict with the entropy increase of the second law, ΔS_{univ} > 0. We explore a recently developed entropy S_{univ}^Q for a pure state and test its behavior in simulations of a model system and environment evolving in time with heat flow to equilibrium. We find that the entropy approaches the correct classical value in a type of classical limit with weak coupling. With stronger coupling, we find a new source of quantum "excess entropy production," which has its origin in the quantum spreading of the wavepacket. Are there quantum thermodynamic effects related to this new source of entropy? To test this, we developed a model for a small variable temperature quantum oscillator bath. We performed simulations where two small baths are linked by a system, with unequal couplings to the baths. The model evolves to a novel type of equilibrium state with unequal temperatures in the baths, with heat flow from cold to hot along the path to equilibrium. We give an account of this behavior in terms of the second law with the quantum entropy S_{univ}^Q. The new formulation of the second law thus appears well-founded and fruitful, with surprising new quantum thermodynamic effects that may still be awaiting discovery, for example in molecules or systems far from equilibrium. \n\nThis dissertation includes previously published and unpublished co-authored material.
In this paper, our focus is on the question whether the cyclic process of coupling and decoupling of a charged quantum magneto-oscillator or a charged quantum electro-oscillator from a quantum heat bath can lead to a violation of the second law of thermodynamics. The results obtained from the thermodynamic entropic point of view are compared with that obtained from the von Neumann entropic perspective. As far as the validity of thermodynamic laws is concerned, the thermodynamic entropy can be chosen judiciously, so that no problem arises in its interpretation.
We study the modification of the second law of thermodynamics for a quantum system interacting with a reservoir regarding quantum coherence. The whole system is isolated so that neither energy nor information is lost. It is discovered that the coherence of the reservoir can serves as a useful resource allowing the system extract more energy from the reservoir; among the coherence measures, only is the relative entropy of coherence feasible to quantitatively characterize energy exchange. We demonstrate that a thermodynamic cycle between two coherent reservoirs can output more work than its classical counterpart. The efficiency of such cycle surpasses the Carnot efficiency, which is the upper bound of heat engine efficiency in classical regime.