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arXiv:1512.06288

Noise-induced Renyi entropy flow of a quantum heat engine

Mohammad H. Ansari

Published Dec 19, 2015• 0 citations
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Abstract

Entropy is one of the central quantities in thermodynamics, whose flow between two systems determines the statistics of energy transfers. In quantum systems entropy is non-linear in density matrix whose time evolution is cumbersome. Using recent developments in the Keldysh formalism for the evolution of nonlinear quantum information measures (Phys. Rev. B 91, 174307 (2015)), we study the flow of von Neumann and Renyi entropies in a generic four-level quantum system that is weakly coupled to equilibrium heat engines. We show that noise-induced coherence has significant influence on the entropy flow of the quantum heat engine. We determine analytical optimization of couplings for the purpose of designing optimal artificial energy transfer systems.

DOI
10.48550/arxiv.1512.06288

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Entropy is one of the central quantities in thermodynamics, whose flow between two systems determines the statistics of energy transfers. In quantum systems entropy is non-linear in density matrix whose time evolution is cumbersome. Using recent developments in the Keldysh formalism for the evolution of nonlinear quantum information measures (Phys. Rev. B 91, 174307 (2015)), we study the flow of von Neumann and Renyi entropies in a generic four-level quantum system that is weakly coupled to equilibrium heat engines. We show that noise-induced coherence has significant influence on the entropy flow of the quantum heat engine. We determine analytical optimization of couplings for the purpose of designing optimal artificial energy transfer systems.
In this work, we study the effect of noise-induced coherence on the performance analysis of a degenerate four-level quantum heat engine with particular focus on the universal nature of efficiency, which refers to the appearance of the first two universal terms ηC/2η_C/2ηC​/2 and ηC2/8η_C^2/8ηC2​/8 in series expansion of the efficiency at maximum power under a left-right symmetry in the system. Firstly, for a two-parameter optimization scheme, we derive an analytic expression for the efficiency at maximum power for the near-equilibrium condition and show that presence of noise-induced coherence breaks the left-right symmetry of the system. However, when the operation of the engine is restricted to either high-temperature or low-temperature regime, we discuss the conditions under which the left-right symmetry can be retained in each case, giving rise to the universal characteristic of efficiency. In case of one-parameter optimization, we show that while the universality of the first linear term ηc/2η_c/2ηc​/2 is robust and holds consistently across all conditions, the universality of the quadratic term ηC2/8η_C^2/8ηC2​/8 depends on the constraints imposed on the control parameters. Finally, we examine the behavior of power as a function of noise-induced coherence parameter highlighting the role of matter-field coupling in determining the suitable operation regime for the heat engine to reap the benefits of noise-induced coherence.
Quantum thermodynamics has emerged as a central field for understanding how energy conversion processes occur in microscopic systems. In these systems, effects such as coherence, entanglement, and non-Markovianity play key roles. In this thesis, we explore different ways to describe quantum thermodynamics, using two main approaches: one based on entropy and the other on ergotropy. First, we introduce a generalized approach to quantify non-Markovianity through the breakdown of monotonicity in thermodynamic functions. In this context, the entropy-based heat flow serves as a practical tool to witness and measure quantum memory in unital maps that do not reverse the sign of the internal energy. Next, we analyze the dynamics of ergotropy in open qubits under both Markovian and non-Markovian evolutions. We identify phenomena such as freezing and sudden death of ergotropy, and we establish an analytical relation between the change in ergotropy and the environment-induced work . This provides a clear physical interpretation for the additional term in the first law in the entropy-based formulation. Finally, we propose an ergotropy-based thermodynamic formulation, in which heat is reinterpreted in terms of the change of the passive state associated with the density operator governing the quantum dynamics. This approach allows one to measure non-Markovianity of unital maps more generally and accurately than the entropy-based heat flow. This advantage comes from the direct link between heat and von Neumann entropy, a property ensured by invariance under passive transformations. Moreover, the out-of-equilibrium temperature naturally remains non-negative, similarly to equilibrium thermodynamics.
We theoretically identify the noise-induced coherent contribution to the ergotropy of a four-level quantum heat engine coupled to a unimodal quantum cavity. We utilize a protocol where the passive state's quasiprobabilities can be analytically identified from the population-coherence coupled reduced density matrix. The reduced density matrix elements are evaluated using a microscopic quantum master equation formalism. Multiple ergotropies within the same coherence interval, each characterized by a positive and pronounced coherent contribution, are observed. These ergotropies are a result of population inversion as well as quasiprobability-population inversion, controllable through the coherence measure parameters. The optimal flux and power of the engine are found to be at moderate values of ergotropy with increasing values of noise-induced coherence. The optimal power at different coherences is found to possess a constant ergotropy.
Thermodynamics of information identifies information flow as a thermodynamic resource, but whether quantum coherence and collective coupling can enhance it at low entropy-production cost remains unresolved. We address this question for interacting open quantum systems by deriving a thermodynamic uncertainty relation that bounds information flow in terms of entropy production in nonequilibrium steady states. We construct a quantum engine in which N-fold degenerate ground and excited states are collectively coupled to heat baths. Collective jumps enhance heat currents and information flow linearly with N, while entropy production remains independent of N, realizing a high-power, low-dissipation autonomous quantum Maxwell's demon that leverages collectively enhanced information flow to pump heat against a temperature gradient. Beyond steady states, collective interactions amplify the unitary component of quantum information flow, yielding a quadratic enhancement of the free-energy charging power of quantum batteries. Our results reveal scalable advantages of quantum coherence and collective effects in quantum engines.
In the present study we have developed an alternative formulation for the quantum stochastic thermodynamics based on the c-number Langevin equation for the system-reservoir model. This is analogous to the classical one. Here we have considered both Markovian and non-Markovian dynamics (NMD). Consideration of the NMD is an important issue at the current state of the stochastic thermodynamics. Applying the present formalism, we have carried out a comparative study on the heat absorbed and the change of entropy with time for a linear quantum system and its classical analog for both Markovian and NMD. Here the strength of the thermal noise and its correlation time for the respective cases are the leading quantities to explain any distinguishable feature which may appear with the equilibration kinetics. For another application, we have proposed a formulation with classical look for a quantum stochastic heat engine. Using it we have presented a comparative study on the efficiency and its value at maximum power for a quantum stochastic heat engine and its classical analog. The engines are Carnot like which are coupled with their respective Markovian thermal baths. Here also the noise strength as well as the diffusion constant are the leading quantities to explain any noticeable feature.