arXiv subjects

Tan Van Vu

Publications and source records attributed to Tan Van Vu.

At least 19 recordsLinked to original sources

arXiv2026

Quantum non-Markovian Hatano-Nelson model

While considering non-Hermitian Hamiltonians arising in the presence of dissipation, in most cases, the dissipation is taken to be frequency independent. However, this idealization may not always be applicable in experimental settings, where dissipation can be frequency-dependent. Such frequency-dependent dissipation leads to non-Markovian behavior. In this work, we demonstrate how a quantum non-Markovian Hatano-Nelson model arises microscopically in a quasi-one-dimensional dissipative lattice. This is achieved using non-equilibrium Green's functions without requiring any approximation like weak system-bath coupling or a time-scale separation, which would have been necessary for a Markovian treatment. The resulting effective system exhibits nonreciprocal hopping, the defining characteristic of the Hatano-Nelson model, as well as uniform dissipation, both of which are frequency-dependent. This holds for both bosonic and fermionic settings. We find solely non-Markovian nonreciprocal features like unidirectional frequency blocking in bosonic settings, and a particular type of non-equilibrium dissipative quantum phase transition in fermionic settings, that cannot be captured in a Markovian theory, nor have any analog in reciprocal systems. Our results lay the groundwork for describing and engineering non-Markovian nonreciprocal quantum lattices.

quant-ph↗

arXiv2026

Exact Fluctuation-Response Relations for Underdamped Langevin Dynamics

Thermodynamic uncertainty relations connect current fluctuations to dissipation and are often rooted in fluctuation-response principles. In underdamped dynamics, however, conventional mean-current uncertainty relations can fail, while the underlying connection between fluctuations, response, and dissipation remains elusive. Here we uncover this structure by deriving an exact finite-time fluctuation-response equality for underdamped Langevin dynamics, valid for arbitrary time-dependent driving and general additive observables. The equality yields sharp response bounds and a variational characterization of the dynamically generated variance. Choosing the perturbation along the irreversible probability flow gives a friction-response thermodynamic uncertainty relation that can be saturated at any finite observation time, leading to an exact variational principle for the total entropy production. We further show that the conventional uncertainty factor of velocity-resolved currents can decay exponentially with dissipation even in driven free diffusion, while the friction-response factor retains its universal lower bound. These results establish response, rather than the mean current itself, as the quantity directly linking fluctuations and dissipation in underdamped dynamics.

cond-mat.stat-mech↗

arXiv2026

The Mpemba effect likes to hit a wall

The original Mpemba effect refers to the idea that a macroscopic hot system cools faster than an initially colder one. In its microscopic and classical versions, the system is modeled as an overdamped particle in an external potential, and the corresponding Mpemba effect has been observed experimentally and explored theoretically. We establish that the existence of the one-dimensional Mpemba effect for a particle in an asymmetric polynomial double-well potential is driven solely by the presence of a hard wall, irrespective of the potential's double-well shape and metastability. The Mpemba effect disappears if we consider an infinitely large system. We then show that the underlying mechanism of the Mpemba effect is governed by the fine structure of the initial statistical population as it probes the tails of the potential, which also explains the Mpemba effect in single-well and symmetric double-well potentials.

cond-mat.stat-mech↗

arXiv2026

Predicting the conditions for observing the Mpemba effect

The Mpemba effect, a counterintuitive phenomenon where a hotter system relaxes faster than a colder one, has been widely observed in various nonequilibrium systems. Despite this progress, the fundamental structural features of the energy landscape required for its emergence remain a subject of debate. In this study, we investigate the conditions for the Mpemba effect within one-dimensional overdamped Langevin dynamics. We classify the potential landscapes based on the presence of single or double wells, their symmetry properties, and the existence of walls. We establish that the existence of the effect is primarily driven by the presence of boundaries, either hard or soft, rather than the specific internal structure of the potential landscape, such as metastability or the number of minima. By employing a spectral decomposition of the Fokker-Planck operator, we analyze the behavior of the first nontrivial eigenmode and demonstrate that its derivative acts as a Dirac delta peak in the low-temperature regime. This helps us elucidate the mechanism underlying the Mpemba effect: it appears as the interplay between this behavior and the initial population dynamics in a non-trivial way induced by the presence of the wall. Our analysis provides a unified classification across single- and double-well potentials, highlighting the crucial role of boundary conditions and asymmetry. Furthermore, we demonstrate that this framework allows for the engineering of potential landscapes capable of producing multistage Mpemba transitions.

cond-mat.stat-mech↗

arXiv2026

Hierarchy of entropy production and thermodynamic trade-off relations in non-Markovian systems

Non-Markovian dynamics arise when a system is coupled to a bath with finite correlation time, producing memory effects that allow the bath to temporarily store and return excitations. However, how memory modifies irreversibility, and whether it can be exploited to improve thermodynamic performance, is not well established. We address this question using a Markovian embedding of generalized Langevin dynamics, in which bath memory is encoded in auxiliary modes and irreversible dissipation is represented by a residual Markovian bath. Here we show that this embedding naturally induces a decomposition of the entropy production of the original non-Markovian system into two parts: the entropy production of the embedded Markovian dynamics, which quantifies the memoryless irreversible contribution, and a nonnegative memory contribution associated with correlations between the system and auxiliary modes. This decomposition establishes a hierarchy of entropy production under Markovian embedding and provides a thermodynamic interpretation of memory effects. The resulting hierarchy yields finite-time thermodynamic bounds for non-Markovian systems, including entropic bounds, thermodynamic uncertainty relations, speed limits, and power-efficiency trade-offs, revealing how memory effects modify heat engine performance and current precision.

cond-mat.stat-mech↗

arXiv2026

Macroscopic Particle Transport in Dissipative Long-Range Bosonic Systems

Dissipation in quantum many-body systems provides a more general and experimentally realistic perspective on particle transport than closed quantum systems. In this work, we determine the maximal speed of macroscopic particle transport in dissipative bosonic systems featuring both long-range hopping and long-range interactions. By developing a generalized optimal transport theory for open quantum systems, we rigorously establish the relationship between the minimum transport time and the source-target distance, and investigate the maximal transportable distance of bosons. We demonstrate that optimal transport exhibits a fundamental distinction depending on whether the system experiences one-body loss or multi-body loss. Moreover, we present the minimal transport time and the maximal transport distance for systems with both gain and loss. We observe that even an arbitrarily small gain rate enables transport over long distances if the lattice gas is dilute. Importantly, we generally reveal that the emergence of decoherence-free subspaces facilitates the long-distance and perfect transport process. Additionally, we derive an upper bound for the probability of transporting a given number of particles during a fixed period in the presence of particle loss. Possible experimental protocols for observing our theoretical predictions are also discussed.

quant-ph↗

arXiv2026

Interplay between Standard Quantum Detailed Balance and Thermodynamically Consistent Entropy Production

We demonstrate that, for a quantum Markovian semigroup on a finite-dimensional Hilbert space, if it satisfies the standard quantum detailed balance condition, its generator admits a special representation that yields a vanishing entropy production rate. Conversely, if the generator admits a special representation adhering to the condition of thermodynamic consistency and leading to a vanishing entropy production rate, then the corresponding quantum Markovian semigroup must satisfy the standard quantum detailed balance condition. In this context, we adopt the definition of entropy production rate that is motivated by the physics literature and standard for thermodynamically consistent Lindbladians.

quant-ph↗

arXiv2026

Geometric complexity in thermodynamics

The third law of thermodynamics forbids cooling a physical system to absolute zero in a finite number of operational steps. Although this unattainability principle has been quantified for specific state-to-state transitions, a universal, dynamics-independent bound for implementing a state-agnostic reset map remains elusive. In this work, we unveil the fundamental limits of physical map implementation by deriving a trade-off relation based on geometric complexity. By analyzing continuous paths of maps on a geometric manifold, we prove that the geometric complexity of any classical stochastic map or quantum channel is bounded from below by its execution error. As a consequence, we show that achieving zero error in a state-reset operation requires a divergent geometric complexity -- a unified measure that naturally incorporates disparate physical resources, including infinite time, energetic cost, or control bandwidth. This unattainability principle holds universally across both classical and quantum regimes, establishing a strict geometric limit on the physical realization of reset operations in thermodynamic control and quantum computation.

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arXiv2026

Universal Precision Limits in General Open Quantum Systems

The intuition that the precision of observables is constrained by thermodynamic costs has recently been formalized through thermodynamic and kinetic uncertainty relations. While such trade-offs have been extensively studied in Markovian systems, corresponding constraints in the non-Markovian regime remain largely unexplored. In this Letter, we derive universal bounds on the precision of generic observables in open quantum systems that interact with their environments at arbitrary coupling strengths and are subjected to two-point measurements. By introducing an asymmetry term that quantifies the disparity between forward and backward processes, we show that the relative fluctuation of any time-antisymmetric current is constrained not only by entropy production but also by this asymmetry. For general observables, we further prove that their relative fluctuation is always bounded from below by a generalized activity term that characterizes environmental changes. These results establish a comprehensive framework for understanding the fundamental limits of precision in a broad class of open quantum systems, beyond the traditional Markovian setting.

quant-ph↗

arXiv2026

Information-thermodynamic bounds on precision in interacting quantum systems

The thermodynamic uncertainty relation quantifies a trade-off between the relative fluctuations of trajectory currents and the thermodynamic cost, indicating that the current precision is fundamentally constrained by entropy production. In classical bipartite systems, it has been shown that information flow between subsystems can enhance the current precision alongside thermodynamic dissipation. In this study, we investigate how information flow, local dissipation, and quantum effects jointly constrain current fluctuations within a subsystem of interacting quantum systems. Unlike classical bipartite systems, quantum subsystems can exhibit simultaneous state changes and maintain quantum coherence, which fundamentally alters the precision-dissipation trade-off. For this general setting, we derive a quantum thermokinetic uncertainty relation for interacting multipartite systems, establishing a thermodynamic trade-off between current fluctuations, information flow, local dissipation, and quantum effects. Our analysis shows that, in addition to local dissipation, both information exchange and quantum coherence play essential roles in suppressing current fluctuations. These results have important implications for the performance of quantum thermal machines, such as information-thermodynamic engines and quantum clocks. We validate our theoretical findings through numerical simulations on two representative models: an autonomous quantum Maxwell's demon and a quantum clock. These results extend uncertainty relations to multipartite open quantum systems and elucidate the functional role of information flow in fluctuation suppression.

quant-ph↗

arXiv2026

Thermodynamic Uncertainty Relation with Quantum Feedback

Fluctuations are intrinsic to microscopic systems and impose fundamental limits on nonequilibrium precision, as captured by the thermodynamic uncertainty relation (TUR), which links current fluctuations to entropy production. While feedback control is expected to further suppress fluctuations, its role within the TUR framework has remained unclear, particularly in quantum systems where control is inherently information-driven. In this Letter, we consider open quantum systems weakly coupled to a thermal environment, in which quantum jumps are continuously monitored, and Markovian feedback is applied. Using quantum mutual information to quantify the information contribution induced by feedback, we derive a finite-time TUR for arbitrary time-integrated currents in terms of entropy production and mutual information. Our results uncover how feedback control suppresses fluctuations together with thermodynamic cost and establishes a fundamental precision bound imposed by information-based control. As an application, we analyze a quantum clock model and demonstrate that the clock precision can be enhanced by feedback control in the presence of a single thermal reservoir.

quant-ph↗

arXiv2026

Roadmap on Quantum Thermodynamics

The last two decades has seen quantum thermodynamics become a well established field of research in its own right. In that time, it has demonstrated a remarkably broad applicability, ranging from providing foundational advances in the understanding of how thermodynamic principles apply at the nano-scale and in the presence of quantum coherence, to providing a guiding framework for the development of efficient quantum devices. Exquisite levels of control have allowed state-of-the-art experimental platforms to explore energetics and thermodynamics at the smallest scales which has in turn helped to drive theoretical advances. This Roadmap provides an overview of the recent developments across many of the field's sub-disciplines, assessing the key challenges and future prospects, providing a guide for its near term progress.

quant-ph↗

arXiv2026

Signatures of coherent initial ensembles on all work moments

Standard treatments of quantum work using projective energy measurements erase initial coherence and alter the dynamics, thereby failing to capture the thermodynamic effects of coherent superpositions of energy eigenstates in an ensemble of initial states. In this article, we use an operational work definition that is non-intrusive, applying it to the case of a driven dissipative qubit, where the qubit's initial preparation comprises coherent superposition states, while the driving is coherence-less. We derive an evolution equation for the moment generating function for this work, faithfully capturing the thermodynamic signature of coherent superpositions in the initial ensemble. We demonstrate that different initial ensembles that correspond to the same density matrix upon ensemble average, while having the same average work, display different work fluctuations. For monotonic driving, we show that fluctuations are maximum for coherence-less initial ensembles. As an application, we consider quantum bit-erasure in finite time and demonstrate significantly different work statistics for erasing a classical bit of information versus a Haar random initial ensemble. Our results indicate that coherence in the initial ensemble can be utilized as a resource for thermodynamic precision without incurring additional dissipative work costs. We also obtain a generalized fluctuation theorem that establishes a new quantum lower bound on the mean dissipated work. This bound, counterintuitively, is also applicable to a "classical" initial ensemble with the same initial density matrix and is connected to quantum absolute irreversibility.

quant-ph↗

arXiv2025

Universal splitting of phase transitions and performance optimization in driven collective systems

Spontaneous symmetry breaking is a hallmark of equilibrium systems, typically characterized by a single critical point separating ordered and disordered phases. Recently, a novel class of non-equilibrium phase transitions was uncovered [Phys. Rev. Res. {\bf 7}, L032049 (2025)], showing that the combined effects of simultaneous contact with thermal baths at different temperatures and external driving forces can split the conventional order-disorder transition into two distinct critical points, determined by which ordered state initially dominates. We show the robustness of this phenomenon by extending a minimal interacting-spin model from the idealized case of simultaneous bath coupling to a finite-time coupling protocol. In particular, we introduce two protocols in which the system interacts with a single bath at a time: a stochastic protocol, where the system randomly switches between the baths at different temperatures, and a deterministic protocol where the coupling alternates periodically. Our analysis reveals two key results: (i) the splitting of phase transitions persists across all coupling schemes -- simultaneous, stochastic, and deterministic -- and (ii) different optimizations of power and efficiency in a collectively operating heat engine reveal that both the stochastic and deterministic protocols exhibit superior global performance at intermediate switching rates and periods when compared to simultaneous coupling. The global trade-off between power and efficiency is described by an expression solely depending on the temperatures of thermal reservoirs as the efficiency approaches to the ideal limit.

cond-mat.stat-mech↗

arXiv2025

Time-cost-error trade-off relation in thermodynamics: The third law and beyond

Elucidating fundamental limitations inherent in physical systems is a central subject in physics. For important thermodynamic operations such as information erasure, cooling, and copying, resources like time and energetic cost must be expended to achieve the desired outcome within a predetermined error margin. In the context of cooling, the unattainability principle of the third law of thermodynamics asserts that infinite "resources" are needed to reach absolute zero. However, the precise identification of relevant resources and how they jointly constrain achievable error remains unclear within the frameworks of stochastic and quantum thermodynamics. In this work, we introduce the concept of separated states, which consist of fully unoccupied and occupied states, and formulate the corresponding thermokinetic cost and error, thereby establishing a unifying framework for a broad class of thermodynamic operations. We then uncover a three-way trade-off relation between time, cost, and error for thermodynamic operations aimed at creating separated states, simply expressed as $τ\mathcal{C}\varepsilon_τ\ge 1-η$. This fundamental relation is applicable to diverse thermodynamic operations, including information erasure, cooling, and copying. It provides a profound quantification of the unattainability principle in the third law of thermodynamics in a general form. Building upon this relation, we explore the quantitative limitations governing cooling operations, the preparation of separated states, and a no-go theorem for exact classical copying. Furthermore, we extend these findings to the quantum regime, encompassing both Markovian and non-Markovian dynamics. Specifically, within Lindblad dynamics, we derive a similar three-way trade-off relation that quantifies the cost of achieving a pure state with a given error.

cond-mat.stat-mech↗

arXiv2025

Fundamental bounds on precision and response for quantum trajectory observables

The precision and response of trajectory observables offer valuable insights into the behavior of nonequilibrium systems. For classical systems, trade-offs between these characteristics and thermodynamic costs, such as entropy production and dynamical activity, have been established through uncertainty relations. Quantum systems, however, present unique challenges, where quantum coherence can enhance precision and violate classical uncertainty relations. In this study, we derive trade-off relations for stochastic observables in Markovian open quantum systems. Specifically, we present three key results: (i) a quantum generalization of the thermo-kinetic uncertainty relation, which bounds the relative fluctuations of currents in terms of entropy production and dynamical activity; (ii) a quantum inverse uncertainty relation, which constrains the relative fluctuations of arbitrary counting observables based on their instantaneous fluctuations and the spectral gap of the symmetrized Liouvillian; and (iii) a quantum response kinetic uncertainty relation, which bounds the response of general observables to kinetic perturbations in terms of dynamical activity. These fundamental bounds, validated numerically using a three-level maser and a boundary-driven XXZ spin chain, provide a comprehensive framework for understanding the interplay between precision, response, and thermodynamic costs in quantum systems.

quant-ph↗

arXiv2025

Thermomajorization Mpemba Effect

The Mpemba effect is a counterintuitive physical phenomenon where a hot system cools faster than a warm one. In recent years, theoretical analyses of the Mpemba effect have been developed for microscopic systems and experimentally verified. However, the conventional theory relies on a specific choice of distance measure to quantify relaxation speed, leading to several theoretical ambiguities. In this Letter, we derive a rigorous quantification of the Mpemba effect based on thermomajorization theory, referred to as the thermomajorization Mpemba effect. This approach resolves all existing ambiguities and provides a unification of the conventional Mpemba effect across all monotone measures. Furthermore, we demonstrate the generality of the thermomajorization Mpemba effect for Markovian dynamics, rigorously proving that it can occur in any temperature regime with fixed energy levels.

cond-mat.stat-mech↗

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↗