arXiv subjects

Keiji Saito

Publications and source records attributed to Keiji Saito.

At least 19 recordsLinked to original sources

arXiv2026

Thermodynamic signatures of the period-doubling route to chemical chaos

Chemical reaction networks can evolve from stable oscillations to chaos through successive period doublings. We investigate general properties of entropy-production fluctuations near the onset of chaos and within the chaotic regime in reversible, well-mixed reaction networks. Near an isolated supercritical period-doubling bifurcation, we find a one-sided divergence of the diffusion constant with exponent one. For chaotic attractors satisfying the stated conditions, the entropy variance per unit volume grows exponentially when the macroscopic limit is taken first. Its exponential growth rate is $2λ_{\max}$, where $λ_{\max}$ is the largest Lyapunov exponent, implying a divergent diffusion constant. We also discuss the volume dependence of the fluctuations and the underlying physical mechanisms.

cond-mat.stat-mech↗

arXiv2026

Exponential clustering of bipartite quantum entanglement at arbitrary temperatures

Macroscopic quantum effects play central roles in the appearance of inexplicable phenomena in low-temperature quantum many-body physics. Such macroscopic quantumness is often evaluated using long-range entanglement, i.e., entanglement in the macroscopic length scale. The long-range entanglement not only characterizes the novel quantum phases but also serves as a critical resource for quantum computation. Thus, the problem that arises is under which conditions can the long-range entanglement be stable even at room temperatures. Here, we show that bi-partite long-range entanglement is unstable at arbitrary temperatures and exponentially decays with distance. Our theorem provides a no-go theorem on the existence of the long-range entanglement. The obtained results are consistent with the existing observations that long-range entanglement at non-zero temperatures can exist in topologically ordered phases, where tripartite correlations are dominant. In the derivation of our result, we introduce a quantum correlation defined by the convex roof of the standard correlation function. We establish an exponential clustering theorem for generic quantum many-body systems for such a quantum correlation at arbitrary temperatures, which yields our main result by relating quantum correlation to quantum entanglement. As a simple application of our analytical techniques, we derived a general limit on the Wigner-Yanase-Dyson skew information and the quantum Fisher information, which will attract significant attention in the field of quantum metrology. Our work reveals novel general aspects of low-temperature quantum physics and sheds light on the characterization of long-range entanglement.

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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 can modify finite-time thermodynamic behavior. We study this problem using a Markovian embedding of generalized Langevin dynamics generated by a Gaussian bath model. We show that the entropy production of the reduced non-Markovian description decomposes into the Markovian entropy production of the enlarged Markovian dynamics and a nonnegative correlation contribution associated with the system-auxiliary modes, establishing a hierarchy of entropy production under Markovian embedding. The resulting hierarchy yields embedding-independent thermodynamic trade-off relations, including entropic bounds, power-efficiency trade-off relations, thermodynamic uncertainty relations, and thermodynamic speed limits. These results clarify how bath memory modifies finite-time constraints on operational speed, engine performance, and current precision. We further show that the entropy-production hierarchy extends beyond Gaussian baths to more general classical and quantum bath models under appropriate thermodynamic conditions.

cond-mat.stat-mech↗

arXiv2026

Exact Fluctuation-Response Relations for Underdamped Langevin Dynamics

Thermodynamic uncertainty relations connect current fluctuations to dissipation and, in certain settings, can emerge from underlying fluctuation-response relations. However, in underdamped dynamics, conventional mean-current uncertainty relations can fail, and the underlying connection between fluctuations, response, and dissipation remains elusive. Here, we uncover this connection by deriving an exact finite-time fluctuation-response equality for underdamped Langevin dynamics, which is 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, we obtain an experimentally accessible friction-response thermodynamic uncertainty relation that is saturable at any finite observation time. It provides both an exact variational principle for entropy production and a weak-noise coherence-dissipation bound for underdamped limit cycles. We further show that the conventional uncertainty factor of velocity-resolved currents can decay exponentially with dissipation, even in driven free diffusion, whereas 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

Looking at bare transport coefficients in fluctuating hydrodynamics

Bare transport coefficients in fluctuating hydrodynamics are not directly observable in bulk systems, as hydrodynamic fluctuations inevitably renormalize them into macroscopic values. In this work, we propose an operational method to determine the bare shear viscosity in two-dimensional dense fluids by focusing on fluid behavior near solid boundaries, where momentum scattering suppresses long-wavelength fluctuations. Using fluctuating hydrodynamic and molecular dynamics simulations supported by analytical arguments, we show that the viscosity measured near walls directly corresponds to the bare value. Based on this observation, we construct a practical protocol to extract the bare viscosity from microscopic data and verify its consistency by predicting flow profiles and equilibrium correlations. We further demonstrate that fluctuating hydrodynamics quantitatively reproduces fluid behavior down to atomic length scales.

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arXiv2026

Symmetry-based nonlinear fluctuating hydrodynamics in one dimension

We present a symmetry-based formulation of nonlinear fluctuating hydrodynamics (NFH) for one-dimensional many-particle systems with generic homogeneous nearest-neighbor interactions. We derive the hydrodynamic equations solely from symmetry and conservation principles, ensuring full consistency with thermalization. Using the dynamic renormalization group, we identify a KPZ-type fixed point, characterized by the dynamical exponent $z=3/2$ for both the sound and heat modes. Extensive numerical simulations of the derived NFH equations confirm this exponent and further reveal that both modes are close to the universal KPZ scaling function, the Prahofer-Spohn function. These findings establish a unified, symmetry-based framework for understanding universal transport and fluctuation phenomena in one-dimensional nonequili brium systems, independent of microscopic details.

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arXiv2026

Universal criticality of entropy production in chemical reaction networks

Stochastic thermodynamics gives universal relations for microscopic entropy production, yet its critical behavior at macroscopic nonequilibrium transitions remains unclassified. We study well-mixed reversible chemical reaction networks in the macroscopic-first limit, where transitions arise as local bifurcations of mass-action dynamics. Using linear-noise formulas, center-manifold normal forms, and Floquet theory, we obtain generic exponents for entropy-production fluctuations and responses at pitchfork, transcritical, saddle-node, and Hopf bifurcations. Beyond this low-order classification, a trajectory-space Cramér-Rao type bound yields the universal scaling inequality $α- 2β\geq 0$. Hence divergent responses require divergent fluctuations, but not conversely, making entropy-production fluctuations a sharper probe of nonequilibrium criticality.

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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.

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arXiv2025

Inverse thermodynamic uncertainty relation and entropy production

Nonequilibrium current fluctuations represent one of the central topics in nonequilibrium physics. The thermodynamic uncertainty relation (TUR) is widely acclaimed for rigorously establishing a lower bound on current fluctuations, expressed in terms of the entropy production rate and the average current. In this study, we focus on an upper bound for the fluctuations, referred to as the inverse thermodynamic uncertainty relation (iTUR). We derive a universal iTUR expression in terms of the entropy production rate for continuous-variable systems governed by overdamped Langevin equations, as well as for discrete-variable systems described by Markov jump processes. The iTUR establishes a no-go theorem prohibiting perpetual superdiffusion in systems with a finite entropy production rate and a finite spectral gap. The divergence of the variance of any current becomes possible only when the spectral gap of the symmetrized time-evolution operator closes or the entropy production rate diverges. As a relevant experimental scenario, we apply the iTUR to the phenomenon of giant diffusion, emphasizing the pivotal roles of the spectral gap and entropy production.

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.

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arXiv2025

Thermal Area Law in Long-Range Interacting Systems

The area law of the bipartite information measure characterizes one of the most fundamental aspects of quantum many-body physics. In thermal equilibrium, the area law for the mutual information universally holds at arbitrary temperatures as long as the systems have short-range interactions. In systems with power-law decaying interactions, $r^{-α}$ ($r$: distance), conditions for the thermal area law are elusive. In this work, we aim to clarify the optimal condition $α> α_c$ such that the thermal area law universally holds. A standard approach to considering the conditions is to focus on the magnitude of the boundary interaction between two subsystems. However, we find here that the thermal area law is more robust than this conventional argument suggests. We show the optimal threshold for the thermal area law by $α_c= (D+1)/2$ ($D$: the spatial dimension of the lattice), assuming a power-law decay of the clustering for the bipartite correlations. Remarkably, this condition encompasses even the thermodynamically unstable regimes $α< D$. We verify this condition numerically, finding that it is qualitatively accurate for both integrable and non-integrable systems. Unconditional proof of the thermal area law is possible by developing the power-law clustering theorem for $α> D$ above a threshold temperature. Furthermore, the numerical calculation for the logarithmic negativity shows that the same criterion $α> (D+1)/2$ applies to the thermal area law for quantum entanglement.

quant-ph↗

arXiv2025

Thermodynamic Uncertainty Relations for Coherent Transport

We derive a universal thermodynamic uncertainty relation for Fermionic coherent transport, which bounds the total rate of entropy production in terms of the mean and fluctuations of a single particle current. This bound holds for any multi-terminal geometry and arbitrary chemical and thermal biases, as long as no external magnetic fields are applied. It can further be saturated in two-terminal settings with boxcar-shaped transmission functions and reduces to its classical counterpart in linear response. Upon insertion of a numerical factor, our bound also extends to systems with broken time-reversal symmetry. As an application, we derive trade-off relations between the figures of merit of coherent thermoelectric heat engines and refrigerators, which show that such devices can attain ideal efficiency only at vanishing mean power or diverging power fluctuations. To illustrate our results, we work out a model of a coherent conductor consisting of a chain of quantum dots.

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arXiv2025

Energy diffusion in the long-range interacting spin systems

We investigate energy diffusion in long-range interacting spin systems, where the interaction decays algebraically as $V(r) \propto r^{-α}$ with the distance $r$ between the sites. We consider prototypical spin systems, the transverse Ising model, and the XYZ model in the $D$-dimensional lattice with finite $α>D$ which guarantees the thermodynamic extensivity. In one dimension, both normal and anomalous diffusion are observed, where the anomalous diffusion is attributed to anomalous enhancement of the amplitude of the equilibrium current correlation. We prove the power-law clustering property of arbitrary orders of joint cumulants in general dimensions. Applying this theorem to equal-time current correlations, we further prove several theorems leading to the statement that the sufficient condition for normal diffusion in one dimension is $α> 3/2$ regardless of the models. The fluctuating hydrodynamics approach consistently explains Lévy diffusion for $α< 3/2$, which implies the condition is optimal. In higher dimensions of $D \geq 2$, normal diffusion is indicated as long as $α> D$.

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arXiv2025

Prethermal inverse Mpemba effect

The inverse Mpemba effect is a counterintuitive phenomenon in which a system, initially in thermal equilibrium and prepared at different temperatures below that of the final equilibrium state, relaxes to the final state more rapidly when starting from a lower initial temperature. We extend this concept to the relaxation toward a prethermal state in isolated quantum systems. By examining a simple model that exhibits prethermalization, we demonstrate that this effect indeed manifests under periodic driving. We further discuss the realization of this phenomenon in a variety of systems within a unified theoretical framework.

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arXiv2025

Thermodynamic bounds and error correction for faulty coarse graining

At the nanoscale, random effects govern not only the dynamics of a physical system but may also affect its observation. This work introduces a novel paradigm for coarse graining that eschews the assignment of a unique coarse-grained trajectory to a microscopic one. Instead, observations are not only coarse-grained but are also accompanied by a small chance of error. Formulating the problem in terms of path weights, we identify a condition on the structure of errors that ensures that the observed entropy production does not increase. As a result, the framework of stochastic thermodynamics for estimating entropy production can be extended to this broader class of systems. As an application, we consider Markov networks in which individual transitions can be observed but may be mistaken for each other. We motivate, derive, and illustrate thermodynamic bounds that relate the error sensitivity of the observed entropy production to the strength of the driving and are valid for arbitrary network topologies. If sufficiently many transitions in the network can be observed, redundancies in the coarse-grained trajectories can be used to detect and correct errors, which potentially improves naive estimates of entropy production. We conclude with an outlook on subsequent research on thermodynamic bounds for erroneous coarse graining.

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arXiv2025

Thermodynamic bound on current fluctuations in coherent conductors

We derive a universal bound on the large-deviation functions of particle currents in coherent conductors. This bound depends only on the mean value of the relevant current and the total rate of entropy production required to maintain a non-equilibrium steady state, thus showing that both typical and rare current fluctuations are ultimately constrained by dissipation. Our analysis relies on the scattering approach to quantum transport and applies to any multi-terminal setup with arbitrary chemical potential and temperature gradients, provided the transmission coefficients between reservoirs are symmetric. This condition is satisfied for any two-terminal system and, more generally, when the dynamics of particles within the conductor are symmetric under time-reversal. For typical current fluctuations, we recover a recently derived thermodynamic uncertainty relation for coherent transport. To illustrate our theory, we analyze a specific model comprising two reservoirs connected by a chain of quantum dots, which shows that our bound can be saturated asymptotically.

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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.

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