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arXiv:1804.06886 · AIP conference proceedings

H-theorem and Maxwell demon in quantum physics

N. S. Kirsanov, A. V. Lebedev, Ivan Sadovskyy, M. V. Suslov, V. M. Vinokur, G. Blatter, Gordey B. Lesovik

Published Jan 1, 2018• 5 citations
arXivHTMLPDF

Abstract

The Second Law of Thermodynamics states that temporal evolution of an isolated system occurs with non-diminishing entropy. In quantum realm, this holds for energy-isolated systems the evolution of which is described by the so-called unital quantum channel. The entropy of a system evolving in a non-unital quantum channel can, in principle, decrease. We formulate a general criterion of unitality for the evolution of a quantum system, enabling a simple and rigorous approach for finding and identifying the processes accompanied by decreasing entropy in energy-isolated systems. We discuss two examples illustrating our findings, the quantum Maxwell demon and heating-cooling process within a two-qubit system.

DOI
10.1063/1.5025464

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The Second Law of Thermodynamics states that temporal evolution of an isolated system occurs with non-diminishing entropy. In quantum realm, this holds for energy-isolated systems the evolution of which is described by the so-called unital quantum channel. The entropy of a system evolving in a non-unital quantum channel can, in principle, decrease. We formulate a general criterion of unitality for the evolution of a quantum system, enabling a simple and rigorous approach for finding and identifying the processes accompanied by decreasing entropy in energy-isolated systems. We discuss two examples illustrating our findings, the quantum Maxwell demon and heating-cooling process within a two-qubit system.
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
The second law of thermodynamics states that the entropy of a closed system is nondecreasing. Discussing the second law in the quantum world poses different challenges and provides different opportunities, involving fundamental quantum-information-theoretic questions and interesting quantum-engineered devices. In quantum mechanics, systems with an evolution described by a so-called unital quantum channel evolve with a nondecreasing entropy. Here, we seek the opposite, a system described by a nonunital and, furthermore, energy-conserving channel that describes a system whose entropy decreases with time. We propose a setup involving a mesoscopic four-lead scatterer augmented by a microenvironment in the form of a spin that realizes this goal. Within this nonunital and energy-conserving quantum channel, the microenvironment acts with two noncommuting operations on the system in an autonomous way. We find that the process corresponds to a partial exchange or swap between the system and environment quantum states, with the system's entropy decreasing if the environment's state is more pure. This entropy-decreasing process is naturally expressed through the action of a quantum Maxwell demon and we propose a quantum-thermodynamic engine with four qubits that extracts work from a single heat reservoir when provided with a reservoir of pure qubits. The special feature of this engine, which derives from the energy conservation in the nonunital quantum channel, is its separation into two cycles, a working cycle and an entropy cycle, allowing us to run this engine with no local waste heat.
The Second Law of thermodynamics states that the entropy of the isolated system is non-diminishing in the course of time evolution. In quantum systems, the Second Law can be violated by adding to the system the quantum Maxwell’s demon (QMD) which reduces entropy without energy exchange. However, extending the system by including into it the QMD itself, restores the Second Law. Remarkably, enlarging system with one more demon we return to the initial situation. Therefore by sequential adding the QMD, we can construct the energy-conserving macroscopic system which evolves in time with decreasing the entropy. Here we demonstrate this general principle on the IBM quantum computer how extending the system by one extra qubit, we still observe the entropy decreasing, thus violating the second law. We utilize five QMD implemented by the extra qubits since decoherence effects restrict the number of possible qubit additions.
Information thermodynamics is a generalization of thermodynamics to quantum systems and includes information as an analogy of negative entropy. This leads to a generalization of the second law in which the presence of quantum information is taken into account. Whether this information corresponds to conscious information, is left open. In an article published by Minagawa et al in Nature, a more rigorous proof than before is represented for the statement that the second law of thermodynamics is also valid in quantum theory with information included. The presence of information makes possible an apparent local violation of the second law in the sense that the system can do more work than the Carnot law allows. However, Maxwell's demon requires metabolic energy to function and it loses it when demonizing. This energy must be compensated and the conclusion is that the second law of thermodynamics is valid.
With a class of quantum heat engines which consists of two-energy-eigenstate systems undergoing, respectively, quantum adiabatic processes and energy exchanges with heat baths at different stages of a cycle, we are able to clarify some important aspects of the second law of thermodynamics. The quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realize Maxwell's demon. While respecting the second law on the average, they are also capable of extracting more work from the heat baths than is otherwise possible in thermal equilibrium.
The second law of classical equilibrium thermodynamics, based on the positivity of entropy production, asserts that any process occurs only in a direction that some information may be lost (flow out of the system) due to the irreversibility inside the system. However, any thermodynamic system can exhibit fluctuations in which negative entropy production may be observed. In particular, in stochastic quantum processes due to quantum correlations and also memory effects we may see the reversal energy flow (heat flow from the cold system to the hot system) and the backflow of information into the system that leads to the negativity of the entropy production which is an apparent violation of the Second Law. In order to resolve this apparent violation, we will try to properly extend the Second Law to quantum processes by incorporating information explicitly into the Second Law. We will also provide a thermodynamic operational meaning for the flow and backflow of information. Finally, it is shown that negative and positive entropy production can be described by a quantum thermodynamic force.