arXiv subjects

Jiming Zheng

Publications and source records attributed to Jiming Zheng.

11 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.

cond-mat.stat-mech↗

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.

cond-mat.stat-mech↗

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.

cond-mat.stat-mech↗

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.

cond-mat.stat-mech↗

arXiv2025

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

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.

cond-mat.stat-mech↗

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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arXiv2024

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.

cond-mat.stat-mech↗

arXiv2022

Fast Functionalization with High Performance in the Autonomous Information Engine

Mandal and Jarzynski have proposed a fully autonomous information heat engine, consisting of a demon, a mass and a memory register interacting with a thermal reservoir. This device converts thermal energy into mechanical work by writing information to a memory register, or conversely, erasing information by consuming mechanical work. Here, we derive a speed limit inequality between the relaxation time of state transformation and the distance between the initial and final distributions, where the combination of the dynamical activity and entropy production plays an important role. Such inequality provides a hint that a speed-performance trade-off relation exists between the relaxation time to functional state and the average production. To obtain fast functionalization while maintaining the performance, we show that the relaxation dynamics of information heat engine can be accelerated significantly by devising an optimal initial state of the demon. Our design principle is inspired by the so-called Mpemba effect, where water freezes faster when initially heated.

cond-mat.stat-mech↗

arXiv2022

Designing Autonomous Maxwell Demon via Stochastic Resetting

Autonomous Maxwell demon is a new type of information engine proposed by Mandal and Jarzynski, which can produce work by exploiting an information tape. Here, we show that a stochastic resetting mechanism can be used to improve the performance of autonomous Maxwell demons notably. Generally, the performance is composed of two important features, the time cost for an autonomous demon to reach its functional state and its efficacious working region in its functional state. Here, we provide a set of design principles for the system, which are capable of improving the two important features. On the one hand, one can drive any autonomous demon system to its functional periodic steady state at a fastest pace for any initial distribution through resetting the demon for a predetermined critical time and closing the reset after that. On the other hand, the system can reach a new functional state when the resetting is always on, in which case the efficacious region of the demon being extended significantly. Moreover, a dual function region in a new phase diagram of the demon with resetting has been found. Remarkably, in this dual function region the demon with resetting can realize anomalous output of work and erasure of information on the tape simultaneously, violating the second law of thermodynamics apparently. To this question, we derive a new modified Clausius inequality to restore the second law by taking the cost of resetting into account.

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