arXiv subjects

Tan Van Vu

Publications and source records attributed to Tan Van Vu.

At least 37 records · Page 2Linked to original sources

arXiv2024

Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach

Understanding the ultimate rate at which information propagates is a pivotal issue in nonequilibrium physics. Nevertheless, the task of elucidating the propagation speed inherent in quantum bosonic systems presents challenges due to the unbounded nature of their interactions. In this study, we tackle the problem of macroscopic particle transport in a long-range generalization of the lattice Bose-Hubbard model through the lens of the quantum speed limit. By developing a unified approach based on optimal transport theory, we rigorously prove that the minimum time required for macroscopic particle transport is always bounded by the distance between the source and target regions, while retaining its significance even in the thermodynamic limit. Furthermore, we derive an upper bound for the probability of observing a specific number of bosons inside the target region, thereby providing additional insights into the dynamics of particle transport. Our results hold true for arbitrary initial states under both long-range hopping and long-range interactions, thus resolving an open problem of particle transport in generic bosonic systems.

quant-ph↗

arXiv2024

Fidelity-dissipation relations in quantum gates

Accurate quantum computing relies on the precision of quantum gates. However, quantum gates in practice are generally affected by dissipative environments, which can significantly reduce their fidelity. In this study, we elucidate fundamental relations between the average fidelity of generic quantum gates and the dissipation that occurs during the computing processes. Considering scenarios in which a quantum gate is subject to Markovian environments, we rigorously derive fidelity-dissipation relations that hold for arbitrary operational times. Intriguingly, when the quantum gate undergoes thermal relaxation, the result can be used as a valuable tool for estimating dissipation through experimentally measurable fidelity, without requiring detailed knowledge of the dissipative structure. For the case of arbitrary environments, we uncover a trade-off relation between the average fidelity and energy dissipation, implying that these quantities cannot be large simultaneously. Our results unveil the computational limitations imposed by thermodynamics, shedding light on the profound connection between thermodynamics and quantum computing.

quant-ph↗

arXiv2024

Geometric characterization for cyclic heat engines far from equilibrium

Considerable attention has been devoted to microscopic heat engines in both theoretical and experimental aspects. Notably, the fundamental limits pertaining to power and efficiency, as well as the tradeoff relations between these two quantities, have been intensively studied. This study aims to shed further light on the ultimate limits of heat engines by exploring the relationship between the geometric length along the path of cyclic heat engines operating at arbitrary speeds and their power and efficiency. We establish a tradeoff relation between power and efficiency using the geometric length and the timescale of the heat engine. Remarkably, because the geometric quantity comprises experimentally accessible terms in classical cases, this relation is useful for the inference of thermodynamic efficiency. Moreover, we reveal that the power of a heat engine is always upper bounded by the product of its geometric length and the statistics of energy. Our results provide a geometric characterization of the performance of cyclic heat engines, which is universally applicable to both classical and quantum heat engines operating far from equilibrium.

cond-mat.stat-mech↗

arXiv2024

Effective light cone and digital quantum simulation of interacting bosons

The speed limit of information propagation is one of the most fundamental features in non-equilibrium physics. The region of information propagation by finite-time dynamics is approximately restricted inside the effective light cone that is formulated by the Lieb-Robinson bound. To date, extensive studies have been conducted to identify the shape of effective light cones in most experimentally relevant many-body systems. However, the Lieb-Robinson bound in the interacting boson systems, one of the most ubiquitous quantum systems in nature, has remained a critical open problem for a long time. This study reveals a tight effective light cone to limit the information propagation in interacting bosons, where the shape of the effective light cone depends on the spatial dimension. To achieve it, we prove that the speed for bosons to clump together is finite, which in turn leads to the error guarantee of the boson number truncation at each site. Furthermore, we applied the method to provide a provably efficient algorithm for simulating the interacting boson systems. The results of this study settle the notoriously challenging problem and provide the foundation for elucidating the complexity of many-body boson systems.

quant-ph↗

arXiv2024

Dissipation, quantum coherence, and asymmetry of finite-time cross-correlations

Recent studies have revealed a deep connection between the asymmetry of cross-correlations and thermodynamic quantities in the short-time limit. In this study, we address the finite-time domain of the asymmetry for both open classical and quantum systems. Focusing on Markovian dynamics, we show that the asymmetry observed in finite-time cross-correlations is upper bounded by dissipation. We prove that, for classical systems in a steady state with arbitrary operational durations, the asymmetry exhibits, at most, linear growth over time, with the growth speed determined by the rates of entropy production and dynamical activity. In the long-time regime, the asymmetry exhibits exponential decay, with the decay rate determined by the spectral gap of the transition matrix. Remarkably, for quantum cases, quantum coherence is equally important as dissipation in constraining the asymmetry of correlations. We demonstrate an example where only quantum coherence bounds the asymmetry while the entropy production rate vanishes. Furthermore, we generalize the short-time bounds on correlation asymmetry, as reported by Shiraishi [Phys. Rev. E 108, L042103 (2023)] and Ohga et al. [Phys. Rev. Lett. 131, 077101 (2023)], to encompass finite-time scenarios. These findings offer novel insights into the thermodynamic aspects of correlation asymmetry.

cond-mat.stat-mech↗

arXiv2023

Universal bounds on the performance of information-thermodynamic engine

We investigate fundamental limits on the performance of information processing systems from the perspective of information thermodynamics. We first extend the thermodynamic uncertainty relation (TUR) to a subsystem. Specifically, for a bipartite composite system consisting of a system of interest X and an auxiliary system Y, we show that the relative fluctuation of an arbitrary current for X is lower bounded not only by the entropy production associated with X but also by the information flow between X and Y. As a direct consequence of this bipartite TUR, we prove universal trade-off relations between the output power and efficiency of an information-thermodynamic engine in the fast relaxation limit of the auxiliary system. In this limit, we further show that the Gallavotti-Cohen symmetry is satisfied even in the presence of information flow. This symmetry leads to universal relations between the fluctuations of information flow and entropy production in the linear response regime. We illustrate these results with simple examples: coupled quantum dots and coupled linear overdamped Langevin equations. Interestingly, in the latter case, the equality of the bipartite TUR is achieved even far from equilibrium, which is a very different property from the standard TUR. Our results will be applicable to a wide range of systems, including biological systems, and thus provide insight into the design principles of biological systems.

cond-mat.stat-mech↗

arXiv2023

Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits

Thermodynamics serves as a universal means for studying physical systems from an energy perspective. In recent years, with the establishment of the field of stochastic and quantum thermodynamics, the ideas of thermodynamics have been generalized to small fluctuating systems. Independently developed in mathematics and statistics, the optimal transport theory concerns the means by which one can optimally transport a source distribution to a target distribution, deriving a useful metric between probability distributions, called the Wasserstein distance. Despite their seemingly unrelated nature, an intimate connection between these fields has been unveiled in the context of continuous-state Langevin dynamics, providing several important implications for nonequilibrium systems. In this study, we elucidate an analogous connection for discrete cases by developing a thermodynamic framework for discrete optimal transport. We first introduce a novel quantity called dynamical state mobility, which significantly improves the thermodynamic uncertainty relation and provides insights into the precision of currents in nonequilibrium Markov jump processes. We then derive variational formulas that connect the discrete Wasserstein distances to stochastic and quantum thermodynamics of discrete Markovian dynamics described by master equations. Specifically, we rigorously prove that the Wasserstein distance equals the minimum product of irreversible entropy production and dynamical state mobility over all admissible Markovian dynamics. These formulas not only unify the relationship between thermodynamics and the optimal transport theory for discrete and continuous cases but also generalize it to the quantum case. In addition, we demonstrate that the obtained variational formulas lead to remarkable applications in stochastic and quantum thermodynamics.

cond-mat.stat-mech↗

arXiv2022

Topological Speed Limit

Any physical system evolves at a finite speed that is constrained not only by the energetic cost but also by the topological structure of the underlying dynamics. In this Letter, by considering such structural information, we derive a unified topological speed limit for the evolution of physical states using an optimal transport approach. We prove that the minimum time required for changing states is lower bounded by the discrete Wasserstein distance, which encodes the topological information of the system, and the time-averaged velocity. The bound obtained is tight and applicable to a wide range of dynamics, from deterministic to stochastic, and classical to quantum systems. In addition, the bound provides insight into the design principles of the optimal process that attains the maximum speed. We demonstrate the application of our results to chemical reaction networks and interacting many-body quantum systems.

quant-ph↗

arXiv2022

Unified thermodynamic-kinetic uncertainty relation

Understanding current fluctuations is of fundamental importance and paves the way for the development of practical applications. According to the thermodynamic and kinetic uncertainty relations, the precision of currents can be constrained solely by total entropy production or dynamical activity. In this study, we derive a tighter bound on the precision of currents in terms of both thermodynamic and kinetic quantities, demonstrating that these quantities jointly constrain current fluctuations. The thermodynamic and kinetic uncertainty relations become particular cases of our result in asymptotic limits. Intriguingly, the unified thermodynamic-kinetic uncertainty relation leads to a tighter classical speed limit, refining the time constraint on the system's state transformation. The proposed framework can be extended to apply to state observables and systems with unidirectional transitions, thereby providing a constraint on the precision of the first-passage time.

cond-mat.stat-mech↗

arXiv2022

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 paper, 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.

cond-mat.stat-mech↗

arXiv2022

Is there any upper bound on current fluctuation in cross-transport beyond linear response regime?

Input and output current fluctuations in stationary cross-transport systems with two kinds of currents are investigated. In Saryal {\it et al.} [Phys. Rev. Lett. 127, 190603 (2021)], upper bounds on input and output current fluctuations are proven in the linear response regime and suggested the validity beyond the linear response regime. We examine these bounds beyond the linear response regime and find that these bounds are violated in general nonequilibrium stationary conditions. We show two examples to demonstrate the violation. Through these examples, we argue that no upper bound on input and output current fluctuations exist beyond the linear response regime.

cond-mat.stat-mech↗

arXiv2021

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 study, 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.

cond-mat.stat-mech↗

arXiv2021

Toward relaxation asymmetry: Heating is faster than cooling

An asymmetry in thermal relaxation toward equilibrium has been uncovered for Langevin systems near stable minima [Phys. Rev. Lett. 125, 110602 (2020)]. It has been shown that, given the same degree of nonequilibrium of the initial distributions, relaxation from a lower temperature state (heating) is faster than that from a higher temperature state (cooling). In this study, we elucidate this relaxation asymmetry for discrete-state Markovian systems described by the master equation. We rigorously prove that heating is faster than cooling for arbitrary two-state systems, whereas for systems with more than two distinct energy levels, the relaxation asymmetry is no longer universal. Furthermore, for systems whose energy levels degenerate into two energy states, we find that there exist critical thresholds of the energy gap. Depending on the magnitude of the energy gap, heating can be faster or slower than cooling, irrespective of the transition rates between states. Our results clarify the relaxation asymmetry for discrete-state systems and reveal several hidden features inherent in thermal relaxation.

cond-mat.stat-mech↗

arXiv2021

Lower Bound on Irreversibility in Thermal Relaxation of Open Quantum Systems

We consider thermal relaxation process of a quantum system attached to a 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 non-unitary dynamics, thus reflecting the dissipative nature of irreversibility. Intriguingly, the bound can be evaluated solely in terms of the initial and final states and the system Hamiltonian; hence, providing a feasible way to estimate entropy production without prior knowledge of the underlying coupling structure. Our finding refines the second law of thermodynamics and reveals a universal feature of thermal relaxation processes.

cond-mat.stat-mech↗

arXiv2020

Geometrical Bounds of the Irreversibility in Markovian Systems

We derive geometrical bounds on the irreversibility in both quantum and classical Markovian open systems that satisfy the detailed balance condition. Using information geometry, we prove that irreversible entropy production is bounded from below by a modified Wasserstein distance between the initial and final states, thus strengthening the Clausius inequality in the reversible-Markov case. The modified metric can be regarded as a discrete-state generalization of the Wasserstein metric, which has been used to bound dissipation in continuous-state Langevin systems. Notably, the derived bounds can be interpreted as the quantum and classical speed limits, implying that the associated entropy production constrains the minimum time of transforming a system state. We illustrate the results on several systems and show that a tighter bound than the Carnot bound for the efficiency of quantum heat engines can be obtained.

cond-mat.stat-mech↗

arXiv2020

Unified Approach to Classical Speed Limit and Thermodynamic Uncertainty Relation

The total entropy production quantifies the extent of irreversibility in thermodynamic systems, which is nonnegative for any feasible dynamics. When additional information such as the initial and final states or moments of an observable is available, it is known that tighter lower bounds on the entropy production exist according to the classical speed limits and the thermodynamic uncertainty relations. Here, we obtain a universal lower bound on the total entropy production in terms of probability distributions of an observable in the time forward and backward processes. For a particular case, we show that our universal relation reduces to a classical speed limit, imposing a constraint on the speed of the system's evolution in terms of the Hatano--Sasa entropy production. Notably, the newly obtained classical speed limit is tighter than the previously reported bound by a constant factor. Moreover, we demonstrate that a generalized thermodynamic uncertainty relation can be derived from another particular case of the universal relation. Our new uncertainty relation holds for systems with time-reversal symmetry breaking and recovers several existing bounds. Our approach provides a unified perspective on two closely related classes of inequality: classical speed limits and thermodynamic uncertainty relations.

cond-mat.stat-mech↗

arXiv2020

Entropy production estimation with optimal current

Entropy production characterizes the thermodynamic irreversibility and reflects the amount of heat dissipated into the environment and free energy lost in nonequilibrium systems. According to the thermodynamic uncertainty relation, we propose a deterministic method to estimate the entropy production from a single trajectory of system states. We explicitly and approximately compute an optimal current that yields the tightest lower bound using predetermined basis currents. Notably, the obtained tightest lower bound is intimately related to the multidimensional thermodynamic uncertainty relation. By proving the saturation of the thermodynamic uncertainty relation in the short-time limit, the exact estimate of the entropy production can be obtained for overdamped Langevin systems, irrespective of the underlying dynamics. For Markov jump processes, because the attainability of the thermodynamic uncertainty relation is not theoretically ensured, the proposed method provides the tightest lower bound for the entropy production. When entropy production is the optimal current, a more accurate estimate can be further obtained using the integral fluctuation theorem. We illustrate the proposed method using three systems: a four-state Markov chain, a periodically driven particle, and a multiple bead-spring model. The estimated results in all examples empirically verify the effectiveness and efficiency of the proposed method.

cond-mat.stat-mech↗

arXiv2019

Uncertainty relation under information measurement and feedback control

Here, we investigate the uncertainty of dynamical observables in classical systems manipulated by repeated measurements and feedback control; the precision should be enhanced in the presence of an external controller but limited by the amount of information obtained from the measurements. We prove that the entropy production and the information quantity constrain from below the fluctuation of arbitrary observables that are antisymmetric under time reversal. The information term is the sum of the mutual entropy production and the Kullback--Leibler divergence, which characterises the irreversibility of the measurement outcomes. The result holds for finite observation times and for both continuous- and discrete-time systems. We apply the derived relation to study the precision of a flashing Brownian ratchet.

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