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Register a new userEntropy production and correlations in a controlled non-Markovian setting
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We study the relationship between (non-)Markovian evolutions, established correlations, and the entropy production rate. We consider a system qubit in contact with a thermal bath and in addition the system is strongly coupled to an ancillary qubit. We examine the steady state properties finding that the coupling leads to effective temperatures emerging in the composite system, and show that this is related to the creation of correlations between the qubits. By establishing the conditions under which the system reaches thermal equilibrium with the bath despite undergoing a non-Markovian evolution, we examine the entropy production rate, showing that its transient negativity is a sufficient sign of non-Markovianity.
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The entropy produced when a quantum system is driven away from equilibrium can be decomposed in two parts, one related with populations and the other with quantum coherences. The latter is usually based on the so-called relative entropy of coherence, a widely used quantifier in quantum resource theories. In this paper we argue that, despite satisfying fluctuation theorems and having a clear resource-theoretic interpretation, this splitting has shortcomings. First, it predicts that at low temperatures the entropy production will always be dominated by the classical term, irrespective of the quantum nature of the process. Second, for infinitesimal quenches, the radius of convergence diverges exponentially as the temperature decreases, rendering the functions non-analytic. Motivated by this, we provide here a complementary approach, where the entropy production is split in a way such that the contributions from populations and coherences are written in terms of a thermal state of a specially dephased Hamiltonian. The physical interpretation of our proposal is discussed in detail. We also contrast the two approaches by studying work protocols in a transverse field Ising chain, and a macrospin of varying dimension.
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Employing the quadratic fermionic Hamiltonians for the collective and internal subsystems with a linear coupling, we studied the role of fermionic statistics on the dynamics of the collective motion. The transport coefficients are discussed as well as the associated fluctuation-dissipation relation. Due to different nature of the particles, the path to equilibrium is slightly affected. However, in the weak coupling regime, the time-scale for approaching equilibrium is found to be globally unchanged. The Pauli-blocking effect can modify the usual picture in open quantum system. In some limits, contrary to boson, this effect can strongly hinder the influence of the bath by blocking the interacting channels.
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We show that non-Markovian effects of the reservoirs can be used as a resource to extract work from an Otto cycle. The state transformation under non-Markovian dynamics is achieved via a two-step process, namely an isothermal process using a Markovian reservoir followed by an adiabatic process. From second law of thermodynamics, we show that the maximum amount of extractable work from the state prepared under the non-Markovian dynamics quantifies a lower bound of non-Markovianity. We illustrate our ideas with an explicit example of non-Markovian evolution.
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