Lower Bound on Irreversibility in Thermal Relaxation of Open Quantum Systems

Emergence of opposing arrows of time in open quantum systems

Deriving an arrow of time from time-reversal symmetric microscopic dynamics is a fundamental open problem in many areas of physics, ranging from cosmology, to particle physics, to thermodynamics and statistical mechanics. Here we focus on the derivation of the arrow of time in open quantum systems and study precisely how time-reversal symmetry is broken. This derivation involves the Markov approximation applied to a system interacting with an infinite heat bath. We find that the Markov approximation does not imply a violation of time-reversal symmetry. Our results show instead that the time-reversal symmetry is maintained in the derived equations of motion. This imposes a time-symmetric formulation of quantum Brownian motion, Lindblad and Pauli master equations, which hence describe thermalisation that may occur into two opposing time directions. As a consequence, we argue that these dynamics are better described by a time-symmetric definition of Markovianity. Our results may reflect on the formulations of the arrow of time in thermodynamics, cosmology, and quantum mechanics.

Efficiency bounds for bipartite information-thermodynamic systems

In this paper, we introduce an approach to derive a lower bound for the entropy production rate of a subsystem by utilizing the Cauchy-Schwarz inequality. It extends to establishing comprehensive upper and lower bounds for the efficiency of two subsystems. These bounds are applicable to a wide range of Markovian stochastic processes, which enhances the accuracy in depicting the range of energy conversion efficiency between subsystems. Empirical validation is conducted using a two-quantum-dot system model, which serves to confirm the effectiveness of our inequality in refining the boundaries of efficiency.

Speed limit, dissipation bound, and dissipation-time trade-off in thermal relaxation processes

We investigate bounds on speed, nonadiabatic entropy production, and the trade-off relation between them for classical stochastic processes with time-independent transition rates. Our results show that the time required to evolve from an initial to a desired target state is bounded from below by the information-theoretical ∞-Rényi divergence between these states, divided by the total rate. Furthermore, we conjecture and provide extensive numerical evidence for an information-theoretical bound on the nonadiabatic entropy production and a dissipation-time trade-off relation that outperforms previous bounds in some cases..

Optimal figure of merit of low-dissipation quantum refrigerators

The Drazin inverse of the Liouvillian superoperator provides a solution to determine the dynamics of a time-dependent system governed by the Markovian master equation. Under the condition of slow driving, the perturbation expansion of the density operator of the system in powers of time can be derived. As an application, a finite-time cycle model of the quantum refrigerator driven by a time-dependent external field is established. The method of the Lagrange multiplier is adopted as a strategy to find the optimal cooling performance. The figure of merit given by the product of the coefficient of performance and the cooling rate is taken as a new objective function, and, consequently, the optimally operating state of the refrigerator is revealed. The effects of the frequency exponent determining dissipation characteristics on the optimal performance of the refrigerator are discussed systemically. The results obtained show that the adjacent areas of the state of the maximum figure of merit are the best operation region of low-dissipative quantum refrigerators.

Geometrical Bounds on Irreversibility in Squeezed Thermal Bath

Irreversible entropy production (IEP) plays an important role in quantum thermodynamic processes. Here, we investigate the geometrical bounds of IEP in nonequilibrium thermodynamics by exemplifying a system coupled to a squeezed thermal bath subject to dissipation and dephasing, respectively. We find that the geometrical bounds of the IEP always shift in a contrary way under dissipation and dephasing, where the lower and upper bounds turning to be tighter occur in the situation of dephasing and dissipation, respectively. However, either under dissipation or under dephasing, we may reduce both the critical time of the IEP itself and the critical time of the bounds for reaching an equilibrium by harvesting the benefits of squeezing effects in which the values of the IEP, quantifying the degree of thermodynamic irreversibility, also become smaller. Therefore, due to the nonequilibrium nature of the squeezed thermal bath, the system-bath interaction energy has a prominent impact on the IEP, leading to tightness of its bounds. Our results are not contradictory with the second law of thermodynamics by involving squeezing of the bath as an available resource, which can improve the performance of quantum thermodynamic devices.

Semi-Markov processes in open quantum systems: Connections and applications in counting statistics

Using the age-structure formalism, we definitely establish connections between semi-Markov processes and the dynamics of open quantum systems that satisfy the Markov quantum master equations. A generalized Feynman-Kac formula of the semi-Markov processes is also proposed. In addition to inheriting all statistical properties possessed by the piecewise deterministic processes of wave functions, the semi-Markov processes show their unique advantages in quantum counting statistics. Compared with the conventional method of the tilted quantum master equation, they can be applied to more general counting quantities. In particular, the terms involved in the method have precise probability meanings. We use a driven two-level quantum system to exemplify these results.

Verification of Information Thermodynamics in a Trapped Ion System

Information thermodynamics has developed rapidly over past years, and the trapped ions, as a controllable quantum system, have demonstrated feasibility to experimentally verify the theoretical predictions in the information thermodynamics. Here, we address some representative theories of information thermodynamics, such as the quantum Landauer principle, information equality based on the two-point measurement, information-theoretical bound of irreversibility, and speed limit restrained by the entropy production of system, and review their experimental demonstration in the trapped ion system. In these schemes, the typical physical processes, such as the entropy flow, energy transfer, and information flow, build the connection between thermodynamic processes and information variation. We then elucidate the concrete quantum control strategies to simulate these processes by using quantum operators and the decay paths in the trapped-ion system. Based on them, some significantly dynamical processes in the trapped ion system to realize the newly proposed information-thermodynamic models is reviewed. Although only some latest experimental results of information thermodynamics with a single trapped-ion quantum system are reviewed here, we expect to find more exploration in the future with more ions involved in the experimental systems.

Quantum Thermodynamics of Holographic Quenches and Bounds on the Growth of Entanglement from the Quantum Null Energy Condition

The quantum null energy condition (QNEC) is a lower bound on the energy-momentum tensor in terms of the variation of the entanglement entropy of a subregion along a null direction. To gain insights into quantum thermodynamics of many-body systems, we study if the QNEC restricts irreversible entropy production in quenches driven by energy-momentum inflow from an infinite memoryless bath in two-dimensional holographic theories. We find that an increase in both entropy and temperature, as implied by the Clausius inequality of classical thermodynamics, is necessary but not sufficient to not violate QNEC in quenches leading to transitions between thermal states with momentums that are dual to Banados-Teitelboim-Zanelli geometries. For an arbitrary initial state, we can determine the lower and upper bounds on the increase of entropy (temperature) for a fixed increase in temperature (entropy). Our results provide explicit instances of quantum lower and upper bounds on irreversible entropy production whose existence has been established in literature. We also find monotonic behavior of the nonsaturation of the QNEC with time after a quench, and analytically determine their asymptotic values. Our study shows that the entanglement entropy of an interval of length l always thermalizes in time l/2 with an exponent 3/2. Furthermore, we determine the coefficient of initial quadratic growth of entanglement analytically for any l, and show that the slope of the asymptotic ballistic growth of entanglement for a semi-infinite interval is twice the difference of the entropy densities of the final and initial states. We determine explicit upper and lower bounds on these rates of growth of entanglement.

Thermodynamics of Precision in Markovian Open Quantum Dynamics

The thermodynamic and kinetic uncertainty relations indicate trade-offs between the relative fluctuation of observables and thermodynamic quantities such as dissipation and dynamical activity. Although these relations have been well studied for classical systems, they remain largely unexplored in the quantum regime. In this Letter, we investigate such trade-off relations for Markovian open quantum systems whose underlying dynamics are quantum jumps, such as thermal processes and quantum measurement processes. Specifically, we derive finite-time lower bounds on the relative fluctuation of both dynamical observables and their first passage times for arbitrary initial states. The bounds imply that the precision of observables is constrained not only by thermodynamic quantities but also by quantum coherence. We find that the product of the relative fluctuation and entropy production or dynamical activity is enhanced by quantum coherence in a generic class of dissipative processes of systems with nondegenerate energy levels. Our findings provide insights into the survival of the classical uncertainty relations in quantum cases.

Finite-Time Quantum Landauer Principle and Quantum Coherence

The Landauer principle states that any logically irreversible information processing must be accompanied by dissipation into the environment. In this Letter, we investigate the heat dissipation associated with finite-time information erasure and the effect of quantum coherence in such processes. By considering a scenario wherein information is encoded in an open quantum system whose dynamics are described by the Markovian Lindblad equation, we show that the dissipated heat is lower bounded by the conventional Landauer cost, as well as a correction term inversely proportional to the operational time. To clarify the relation between quantum coherence and dissipation, we derive a lower bound for heat dissipation in terms of quantum coherence. This bound quantitatively implies that the creation of quantum coherence in the energy eigenbasis during the erasure process inevitably leads to additional heat costs. The obtained bounds hold for arbitrary operational time and control protocol. By following an optimal control theory, we numerically present an optimal protocol and illustrate our findings by using a single-qubit system.