arXiv subjects

Zhiyue Lu

Publications and source records attributed to Zhiyue Lu.

At least 19 recordsLinked to original sources

arXiv2026

The Memory Hidden in Response Fluctuations: Trajectory-Level Fluctuation-Response Theory and Inequalities for Non-Markovian Jump Dynamics

Modern experiments often record nonequilibrium dynamics as sequences of discrete events whose rates depend on the realized past. We develop a fluctuation-response theory for such non-Markovian jump processes directly on the observed event record. Memory can destroy a closed master equation for the state probabilities. Each transition count nevertheless obeys an exact stochastic equation. After the history-dependent mean event tendency is subtracted, the remaining random increment is a martingale increment--the part of the event that cannot be predicted from the past. Martingale increments associated with different transitions and different times are orthogonal. These increments form a complete orthogonal basis for the random deviation of any observable measured from the record, such as a current, occupation time, or event count. The coefficient of a given increment is the event-consequence kernel. It measures how that event changes the predicted final observable, relative to continuing without the event, for the particular history already realized. Multiplying this kernel by the event intensity gives the history-conditioned response to perturbing the corresponding transition rate. Thus, the intensity-normalized response is exactly the expansion coefficient of that event in the observable fluctuation. This identification yields exact finite-time and finite-frequency fluctuation-response relations. Averaging over histories leaves a nonnegative response-heterogeneity gap. The gap measures how strongly the consequence of the same event varies across histories and tests whether a proposed memory coordinate is response-sufficient. Finite-history versions can be estimated from spontaneous trajectories. Bounding the logarithmic rate sensitivity further gives response-kinetic uncertainty relations controlled by dynamical activity.

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arXiv2026

Slow is fast: raising barriers to accelerate thermal relaxation

For a reversible system relaxing to equilibrium, the obvious fastest strategy is to lower all kinetic barriers (open all gates). We find that such intuition holds at three levels: the all-open-gate strategy achieves the highest local conductance, it maximizes the instantaneous speed of approach in every $f$-divergence, and it simultaneously maximizes all relaxation eigenvalues. Nevertheless, we show that a counter-intuitive finite-time optimum lies beyond this intuition and operates at a fourth level, invisible to all three: eigenvector rotation. Noncommutativity enables timed schedules to reproject residual amplitudes across relaxation modes, thereby achieving faster relaxation. Optimal schedules are bang--bang. In our illustrative example, the best-found schedule also employs counter-gating, transiently raising selected barriers, and reduces the terminal residual by a factor of $130$ relative to all-open, and by $7$ relative to the best static landscape. A no-go theorem shows that noncommutativity is necessary: commuting generators collapse every schedule to a static time-averaged landscape, worse than the intuitive static control. In the reverse problem, the dual schedule preserves nonequilibrium free energy far more effectively than intuitively keeping all barriers at maximum heights. Whether accelerating or delaying relaxation, barrier control performs no work on the reduced Markov system; it only re-times a fixed total dissipation budget.

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arXiv2026

Mutual Linearity in and out of Stationarity for Markov Jump Processes: A Trajectory-Based Approach

Nonequilibrium response theory is a fundamental framework for understanding how physical systems respond to perturbations. Recently, a mutual linearity has been discovered for Markov jump processes using linear algebra analysis. This mutual linearity states that two observables are linearly dependent on each other in the long-time limit when the transition rate of a single edge is altered. It has also been extended to non-stationary cases for current observables. In this work, we provide a trajectory-based derivation of mutual linearity utilizing the trajectory-level linear response theory. The trajectory approach allows us to generalize the mutual linearity to non-stationary relaxation dynamics for state observables and counting observables. Our results shed light on the fundamental response properties far from equilibrium and the trajectory-level origin of mutual linearity. Our trajectory-based approach makes it possible to generalize the mutual linearity to a broader class of systems, including diffusion processes and open quantum systems.

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arXiv2026

Spectral Duality and Thermodynamic Bounds on Finite-frequency Fluctuation Responses

Fluctuation-response relations encode fundamental constraints on non-equilibrium systems. While time-domain static response is bounded by activity and entropy production, finite-frequency thermodynamic bounds for time-dependent perturbations remain largely unexplored. Here, we find a finite-frequency response-duality relation in non-equilibrium Markov jump processes. For state-current observables, the ratio between the spectral responses to kinetic-barrier and entropic-force perturbations is frequency-independent and gives the single-transition entropy production. The response-duality relation provides a method for measuring the single-transition entropy production from spectral response signals. Furthermore, we derive frequency-domain thermodynamic and kinetic inequalities for non-equilibrium systems with time-dependent perturbations around unperturbed steady states. We illustrate our response-duality relation on a quantum dot system. These finite-frequency response relations and inequalities provide a practical route for inferring dissipation from power-spectrum response measurements.

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arXiv2026

Fröhlich Condensation of Bosons: Graph texture of curl flux network for nonequilibrium properties

Nonequilibrium condensates of bosons subject to energy pump and dissipation are investigated, manifesting the Fröhlich coherence proposed in 1968. A quantum theory is developed to capture such a nonequilibrium nature, yielding a certain graphic structure arising from the detailed-balance breaking. The results show a network of probability curl fluxes that reveals a graph topology. The winding number associated with the flux network is thus identified as a new order parameter for the phase transition towards the Fröhlich condensation (FC), not attainable by the symmetry breaking. Our work demonstrates a global property of the FCs, in significant conjunction with the coherence of cavity polaritons that may exhibit robust cooperative phases driven far from equilibrium.

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arXiv2026

Mutual Linearity in Nonequilibrium Langevin Dynamics

Understanding how nonequilibrium systems respond to perturbations is a central challenge in physics. In this work, we establish mutual linearity in nonequilibrium overdamped Langevin systems. This theory provides a framework for controlling and designing nonequilibrium responses in continuous systems. When a dynamical parameter is locally perturbed at a single position, the stationary densities at any two positions are linearly related. It further leads to mutual linearity among different stationary state-current observables. We also extend the mutual linearity to non-stationary relaxation processes in the Laplace domain. Our theory reveals that mutual linearity in both discrete and continuous systems originates from the same one-dimensional response structure. We further show that mutual linearity is robust under finite-width perturbations. As an application, we demonstrate the mutual linearity and its finite-width robustness in the F$_1$-ATPase rotary motor model.

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arXiv2026

Nonlinear Response Relations and Fluctuation-Response Inequalities for Nonequilibrium Stochastic Systems

Predicting how systems respond to external perturbations far from equilibrium remains a fundamental challenge across physics, chemistry, and biology. We present a unified response framework for stochastic Markov dynamics that integrates linear and nonlinear perturbations. Our formalism expresses nonlinear responses of observables in terms of the covariance between the observable and a nonlinear conjugate variable. The nonlinear conjugate variable is subject to the complete Bell polynomial form and is determined by the stochastic entropy production. In addition, the Fluctuation-Response Inequalities (FRIs) are also derived for nonlinear responses, unraveling the general trade-off relations between nonlinear response and systems' fluctuations far from equilibrium. The validity of our theory is verified by the numerical results from a symmetric exclusion process (SEP). By unifying and extending nonequilibrium linear response theories, our approach can provide principled design rules for sensitive, adaptive synthetic and biological networks.

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arXiv2025

Nonequilibrium Macroscopic Response Relations for Counting Statistics

Understanding how macroscopic nonequilibrium systems respond to changes in external or internal parameters remains a fundamental challenge in physics. In this work, we report a parameter transitional symmetry valid for macroscopic dynamics arbitrarily far from equilibrium. The symmetry leads to exact response relations and gives meaningful expansions in both linear and short-time regimes. This framework provides a universal description of macroscopic response phenomena arbitrarily far from equilibrium - including non-stationary processes and time-dependent attractors. The theory is validated and demonstrated numerically using the Willamowski-Rossler model, which exhibits rich dynamical behaviors including limit cycles and chaos.

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arXiv2025

Unified Linear Fluctuation-Response Theory Arbitrarily Far from Equilibrium

Understanding how systems respond to external perturbations is a fundamental challenge in physics, particularly for non-equilibrium and non-stationary processes. The fluctuation-dissipation theorem provides a complete framework for near-equilibrium systems, and various bounds have recently been reported for specific non-equilibrium regimes. Here, we present an exact response equality for arbitrary Markov processes that decompose system response into spatial correlations of local dynamical events. This decomposition reveals that response properties are encoded in correlations between transitions and dwelling times across the network, providing a natural generalization of the fluctuation-dissipation theorem and recently developed non-equilibrium linear response relations. Our theory unifies existing response bounds, extends them to time-dependent processes, and reveals fundamental monotonicity properties of the tightness of multi-parameter response inequalities. Beyond its theoretical significance, this framework enables efficient numerical evaluation of response properties from sampling unperturbed trajectories, offering significant advantages over traditional finite-difference approaches for estimating response properties of complex networks and biological systems far from equilibrium.

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arXiv2025

Universal Response Inequalities Beyond Steady States via Trajectory Information Geometry

Fluctuation-dissipation relations elucidate the response of near-equilibrium systems to environmental changes, with recent advances extending response theory to non-equilibrium steady states. However, a general response theory for systems evolving far from steady states has remained elusive. This letter presents a complete trajectory information geometric framework that generalizes response theory for non-stationary Markov processes. By constructing the full trajectory probability manifold and identifying a globally orthogonal coordinate system defined by transition rates, we derive a diagonal Fisher information metric that enables explicit calculations in this high-dimensional space. From the local metric structure, we obtain a Cramer-Rao-type inequality that bounds the linear response of arbitrary non-stationary observables. Furthermore, by analyzing the global geometry of this manifold, we derive a universal non-perturbative (nonlinear) response inequality in terms of geodesic length. This geometric framework reveals deep connections between dynamical activity, observable variance, and system sensitivity, and it encompasses or anticipates several recent results as special cases. Our approach offers new design principles for responsive behaviors in far-from-equilibrium systems.

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arXiv2024

Single-molecule Automata: Harnessing Kinetic-Thermodynamic Discrepancy for Temporal Pattern Recognition

Molecular-scale computation is crucial for smart materials and nanoscale devices, yet creating single-molecule systems capable of complex computations remains challenging. We present a theoretical framework for a single-molecule computer that performs temporal pattern recognition and complex information processing. Our approach introduces the concept of an energy seascape, extending traditional energy landscapes by incorporating control parameter degrees of freedom. By engineering a kinetic-thermodynamic discrepancy in folding dynamics, we demonstrate that a linear polymer with $N$ binary-state foldable units can function as a deterministic finite automaton, processing $2^N$ configurations. The molecule's dominant configuration evolves deterministically in response to mechanical signals, enabling recognition of complex temporal patterns. This design allows complete state controllability through non-equilibrium driving protocols. Our model opens avenues for molecular-scale computation with applications in biosensing, smart drug delivery, and adaptive materials. We discuss potential experimental realizations using DNA nanotechnology. This work bridges the gap between information processing devices and stochastic molecular systems, paving the way for sophisticated molecular computers rivaling biological systems in complexity and adaptability.

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arXiv2024

Revisiting Kinetic Monte Carlo Algorithms for Time-dependent Processes: from open-loop control to feedback control

Simulating stochastic systems with feedback control is challenging due to the complex interplay between the system's dynamics and the feedback-dependent control protocols. We present a single-step-trajectory probability analysis to time-dependent stochastic systems. Based on this analysis, we revisit several time-dependent kinetic Monte Carlo (KMC) algorithms designed for systems under open-loop-control protocols. Our analysis provides an unified alternative proof to these algorithms, summarized into a pedagogical tutorial. Moreover, with the trajectory probability analysis, we present a novel feedback-controlled KMC algorithm that accurately captures the dynamics systems controlled by external signal based on measurements of the system's state. Our method correctly captures the system dynamics and avoids the artificial Zeno effect that arises from incorrectly applying the direct Gillespie algorithm to feedback-controlled systems. This work provides a unified perspective on existing open-loop-control KMC algorithms and also offers a powerful and accurate tool for simulating stochastic systems with feedback control.

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arXiv2024

Information Benchmark for Biological Sensors Beyond Steady States -- Mpemba-like sensory withdrawal effect

Biological sensors rely on the temporal dynamics of ligand concentration for signaling. The sensory performance is bounded by the distinguishability between the sensory state transition dynamics under different environmental protocols. This work presents a comprehensive theory to characterize arbitrary transient sensory dynamics of biological sensors. Here the sensory performance is quantified by the Kullback-Leibler (KL) divergence between the probability distributions of the sensor's stochastic paths. We introduce a novel benchmark to assess a sensor's transient sensory performance arbitrarily far from equilibrium. We identify a counter-intuitive phenomenon in multi-state sensors: while an initial exposure to high ligand concentration may hinder a sensor's sensitivity towards a future concentration up-shift, certain sensors may show a boost in sensitivity if the initial high concentration exposure is followed by a transient resetting at a low concentration environment. The boosted performance exceeds that of a sensor starting from an initially low concentration environment. This effect, reminiscent of a drug withdrawal effect, can be explained by the Markovian dynamics of the multi-state sensor, similar to the Markovian Mpemba effect. Moreover, an exhaustive machine learning study of 4-state sensors reveals a tight connection between the sensor's performance and the structure of the Markovian graph of its states.

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arXiv2024

Stochastic Distinguishability of Markovian Trajectories

The ability to distinguish between stochastic systems based on their trajectories is crucial in thermodynamics, chemistry, and biophysics. The Kullback-Leibler (KL) divergence, $D_{\text{KL}}^{AB}(0,τ)$, quantifies the distinguishability between the two ensembles of length-$τ$ trajectories from Markov processes A and B. However, evaluating $D_{\text{KL}}^{AB}(0,τ)$ from histograms of trajectories faces sufficient sampling difficulties, and no theory explicitly reveals what dynamical features contribute to the distinguishability. This letter provides a general formula that decomposes $D_{\text{KL}}^{AB}(0,τ)$ in space and time for any Markov processes, arbitrarily far from equilibrium or steady state. It circumvents the sampling difficulty of evaluating $D_{\text{KL}}^{AB}(0,τ)$. Furthermore, it explicitly connects trajectory KL divergence with individual transition events and their waiting time statistics. The results provide insights into understanding distinguishability between Markov processes, leading to new theoretical frameworks for designing biological sensors and optimizing signal transduction.

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arXiv2023

Non-equilibrium Theoretical Framework and Universal Design Principles of Oscillation-Driven Catalysis

At stationary environmental conditions, a catalyst's reaction rates may be restricted by thermodynamic laws, and certain performances can never be achieved (e.g., catalysts can not change the free energy difference between reactants and products). However, it has been reported that if environments change rapidly, catalysts can be driven away from stationary states and exhibit anomalous performance. We present a general geometric non-equilibrium theory to describe and explain anomalous catalytic behaviors in rapidly oscillating environments that exceed the steady-state restrictions. It leads to a universal design principle of novel catalysts with oscillation-pumped performances. Even though a catalyst at various environmental conditions cannot be described by a single free energy landscape, we propose a novel control-conjugate landscape to encode the reaction rates over a continuous range of control parameters $λ$, which is inspired by the exponential form of the Arrhenius law. The control-conjugate landscape significantly simplifies the design principle and makes it applicable to large-amplitude environmental oscillations. The design principle is demonstrated by two examples, (1) inverting a spontaneous reaction to synthesize high-free-energy molecules and (2) speeding up reactions without utilizing low activation barriers. In both examples, catalysts autonomously harness energy from non-equilibrium environments to enable such functionalities.

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arXiv2023

Geometric approach to nonequilibrium hasty shortcuts

Complex and even non-monotonic responses to external control can be found in many thermodynamic systems. In such systems, non-equilibrium shortcuts can rapidly drive the system from an initial state to a desired final state. One example is the Mpemba effect, where pre-heating a system allows a system to cool faster. We present nonequilibrium hasty shortcuts -- externally controlled temporal protocols that rapidly steer a system from an initial steady state to a desired final steady state. The term ``hasty'' indicates that the shortcut only involves fast dynamics without relying on slow relaxations. We provide a geometric analysis of such shortcuts in the space of probability distributions by using time-scale separation and eigenmode decomposition. We further identify the necessary and sufficient condition for the existence of non-equilibrium hasty shortcuts in an arbitrary system. The geometric analysis within the probability space sheds light on the possible features of a system that can lead to hasty shortcuts, which can be classified into different categories based on their temporal pattern. We also find that the Mpemba-effect-like shortcuts only constitute a small fraction of the diverse categories of hasty shortcuts. This theory is validated and illustrated numerically in the self-assembly model inspired by viral capsid assembly processes.

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arXiv2023

Theoretical upper bound of multiplexing in stochastic sensory receptors

Biological sensory receptors provide excellent examples of microscopic scale information transduction amidst stochastic noise. We argue that stochasticity is not always a hindrance to sensing. Instead, it could allow a single stochastic sensor to perform multiplexing: simultaneously transducing multiple types of environmental information to the downstream sensory network. Through a Langevin dynamics simulation of a ligand-receptor sensor in a bath of ligands, we demonstrate that a binary-state receptor can simultaneously encode multiple independent environmental variables, such as ligand concentration and the speed of media flow. We develop a general theory of stochastic sensory multiplexing and suggest two theoretical upper bounds. Furthermore, we conjecture that randomly generated sensors typically saturate the tighter upper bound. The theoretical framework developed in this study, which involves a rank-deficient maximum likelihood analysis (rd-MLE), provides a systematic approach to comprehensively assess a sensor's sensory ability without any initial assumptions. This theoretical framework can inspire the design of more efficient artificial sensors.

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arXiv2022

Energy Landscape Design Principle for Optimal Energy Harnessing by Catalytic Molecular Machines

Under temperature oscillation, cyclic molecular machines such as catalysts and enzymes could harness energy from the oscillatory bath and use it to drive other processes. Using a novel geometrical approach, under fast temperature oscillation, we derive a general design principle for obtaining the optimal catalytic energy landscape that can harness energy from a temperature-oscillatory bath and use it to invert a spontaneous reaction. By driving the reaction against the spontaneous direction, the catalysts convert low free energy product molecules to high free energy reactant molecules. The design principle, derived for arbitrary cyclic catalysts, is expressed as a simple quadratic objective function that only depends on the reaction activation energies, and is independent of the temperature protocol. Since the reaction activation energies are directly accessible by experimental measurements, the objective function can be directly used to guide the search for optimal energy-harvesting catalysts.

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