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arXiv:2203.14766 · Physical review. E

Upper bound for quantum entropy production from entropy flux

Domingos S. P. Salazar

Published Apr 1, 2022• 4 citations
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Abstract

Entropy production is a key quantity characterizing nonequilibrium systems. However, it can often be difficult to compute in practice, as it requires detailed information about the system and the dynamics it undergoes. This becomes even more difficult in the quantum domain and if one is interested in generic nonequilibrium reservoirs, for which the standard thermal recipes no longer apply. In this paper, we derive an upper bound for the entropy production in terms of the entropy flux for a class of systems for which the flux is given in terms of a system's observable. Since currents are often easily accessible in this class of systems, this bound should prove useful for estimating the entropy production in a broad variety of processes. We illustrate the applicability of the bound by considering a three-level maser engine and a system interacting with a squeezed bath.

DOI
10.1103/physreve.105.l042101

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Entropy production is a key quantity characterizing nonequilibrium systems. However, it can often be difficult to compute in practice, as it requires detailed information about the system and the dynamics it undergoes. This becomes even more difficult in the quantum domain and if one is interested in generic nonequilibrium reservoirs, for which the standard thermal recipes no longer apply. In this paper, we derive an upper bound for the entropy production in terms of the entropy flux for a class of systems for which the flux is given in terms of a system's observable. Since currents are often easily accessible in this class of systems, this bound should prove useful for estimating the entropy production in a broad variety of processes. We illustrate the applicability of the bound by considering a three-level maser engine and a system interacting with a squeezed bath.
In quantum systems, entropy production is typically defined as the quantum relative entropy between two states. This definition provides an upper bound for any flux (of particles, energy, entropy, etc.) of bounded observables, which proves especially useful near equilibrium. However, this bound tends to be irrelevant in general nonequilibrium situations. We propose a new upper bound for such fluxes in terms of quantum relative entropy, applicable even far from equilibrium and in the strong coupling regime. Additionally, we compare this bound with Monte Carlo simulations of random qubits with coherence, as well as with a model of two interacting nuclear spins.
We consider the thermal relaxation process of a quantum system attached to single or multiple reservoirs. Quantifying the degree of irreversibility by entropy production, we prove that the irreversibility of the thermal relaxation is lower bounded by a relative entropy between the unitarily evolved state and the final state. The bound characterizes the state discrepancy induced by the nonunitary dynamics, and thus reflects the dissipative nature of irreversibility. Intriguingly, the bound can be evaluated solely in terms of the initial and final states and the system Hamiltonian, thereby providing a feasible way to estimate entropy production without prior knowledge of the underlying coupling structure. This finding refines the second law of thermodynamics and reveals a universal feature of thermal relaxation processes.
Abstract The entropy production rate is a key quantity in nonequilibrium thermodynamics of both classical and quantum processes. No universal theory of entropy production is available to date, which hinders progress toward its full grasping. By using a phase space-based approach, here we take the current framework for the assessment of thermodynamic irreversibility all the way to quantum regimes by characterizing entropy production—and its rate—resulting from the continuous monitoring of a Gaussian system. This allows us to formulate a sharpened second law of thermodynamics that accounts for the measurement back action and information gain from a continuously monitored system. We illustrate our framework in a series of physically relevant examples.
A fluctuation theorem for the nonequilibrium entropy production in quantum phase space is derived, which enables the consistent thermodynamic description of arbitrary quantum systems, open and closed. The new treatment naturally generalizes classical results to the quantum domain. As an illustration the harmonic oscillator dragged through a thermal bath is solved numerically. Finally, the significance of the new approach is discussed in detail, and the phase space treatment is opposed to the two-time energy measurement approach.
The characterization of irreversibility in general quantum processes is an open problem of increasing technological relevance. Yet, the tools currently available to this aim are mostly limited to the assessment of dynamics induced by equilibrium environments, a situation that often does not match the reality of experiments at the microscopic and mesoscopic scale. We propose a theory of irreversible entropy production that is suited for quantum systems exposed to general, nonequilibrium reservoirs. We illustrate our framework by addressing a set of physically relevant situations that clarify both the features and the potential of our proposal.
In this paper, we have studied the Shannon "entropic" nonequilibrium temperature (NET) of quantum Brownian systems. The Brownian particle is attached to either a bosonic or fermionic bath. Based on the Fokker-Planck description of the c-number quantum Langevin equation, we have calculated entropy production, NET, and their bounds. Entropy production (EP), the upper bound of entropy production (UBEP), and the deviation of the UBEP from EP monotonically decrease as functions of time to equilibrium value for both of the thermal baths. The deviation decreases with increase of temperature of the bosonic thermal bath, but it becomes larger as the temperature of the fermionic bath grows. We also observe that nonequilibrium temperature and its lower bound monotonically increase to equilibrium value with the progression of time. But their difference as a function of time shows an optimum behavior in most cases. Finally, we have observed that at long time, the entropic temperature (for a bosonic thermal bath) first increases nonlinearly as a function of thermodynamic temperature (TT) and, if the TT is appreciably large, then it grows linearly. But for the fermionic thermal bath, the entropic temperature decreases monotonically as a nonlinear function of thermodynamic temperature to zero value.