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Event cameras capture the motion of intensity gradients (edges) in the image plane in the form of rapid asynchronous events. When accumulated in 2D histograms, these events depict overlays of the edges in motion, consequently obscuring the spatial structure of the generating edges. Contrast maximization (CM) is an optimization framework that can reverse this effect and produce sharp spatial structures that resemble the moving intensity gradients by estimating the motion trajectories of the events. Nonetheless, CM is still an underexplored area of research with avenues for improvement. In this paper, we propose a novel hybrid approach that extends CM from uni-modal (events only) to bi-modal (events and edges). We leverage the underpinning concept that, given a reference time, optimally warped events produce sharp gradients consistent with the moving edge at that time. Specifically, we formalize a correlation-based objective to aid CM and provide key insights into the incorporation of multiscale and multireference techniques. Moreover, our edge-informed CM method yields superior sharpness scores and establishes new state-of-the-art event optical flow benchmarks on the MVSEC, DSEC, and ECD datasets., Comment: To be published in the 2025 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV)

We consider Riesz energy problems with radial external fields. We study the question of whether or not the equilibrium is the uniform distribution on a sphere. We develop general necessary as well as general sufficient conditions on the external field that apply to powers of the Euclidean norm as well as certain Lennard--Jones type fields. Additionally, in the former case, we completely characterize the values of the power for which dimension reduction occurs in the sense that the support of the equilibrium measure becomes a sphere. We also briefly discuss the relation between these problems and certain constrained optimization problems. Our approach involves the Frostman characterization, the Funk--Hecke formula, and the calculus of hypergeometric functions., Comment: 34 pages, 6 figures

We study the non-equilibrium work in a pedagogical model of relativistic ideal gas. We obtain the exact work distribution and verify the Jarzynski's equality. In the non-relativistic limit, our results recover the non-relativistic results [arXiv:cond-mat/0502434]. We also find that, unlike the non-relativistic case, the work distribution no longer has zeros and the number of collisions in this relativistic gas model is finite. In addition, based on an analysis of the experimental parameters, we conclude that it is difficult to detect the relativistic effects of the work distribution of the ideal gas in a piston system with the current experimental techniques.

The theory of equilibrium phase transition, which traditionally does not involve time evolution, concerns only static quantities. In recent decades, owing to the development of nonequilibrium thermodynamics, there is a growing interest in nonequilibrium phase transition which concerns time evolution. It is well-known that in the absence of phase transitions, the excess work resulted from finite-rate quench is proportional to the quench rate v. The time evolution in a second-order phase transition can be understood via the Kibble-Zurek mechanism, and the scaling of work is related to the critical exponents. Nevertheless, the finite-time nonequilibrium thermodynamics of the first-order phase transition remains largely unexplored. We investigate the scaling relations of some thermodynamic quantities with the quench rate in the first-order phase transition. It is shown that the excess work scales as $v^{2/3}$ for small quench rate. Moreover, the delay time and the transition time scale as $v^{1/3}$. Our study deepens the understanding about the nonequilibrium thermodynamics of the first-order phase transition.

The principle of covariance, a cornerstone of modern physics, asserts the equivalence of all inertial frames of reference. Fluctuation theorems, as extensions of the second law of thermodynamics, establish universal connections between irreversibility and fluctuation in terms of stochastic thermodynamic quantities. However, these relations typically assume that both the thermodynamic system and the heat bath are at rest with respect to the observer, thereby failing to satisfy the principle of covariance. In this study, by introducing covariant work and heat that incorporate both energy-related and momentum-related components, we promote fluctuation theorems into covariant forms applicable to moving thermodynamic systems and moving heat baths. We illustrate this framework with two examples: the work statistics of a relativistic stochastic field and the heat statistics of a relativistic Brownian motion. Although our study is carried out in the context of special relativity, the results can be extended to the nonrelativistic limit. Our work combines the principle of covariance and fluctuation theorems into a coherent framework and may have applications in the study of thermodynamics relevant to cosmic microwave background as well as the radiative heat transfer and noncontact friction between relatively moving bodies.

The pursuit of achieving the maximum power in microscopic thermal engines has gained increasing attention in recent studies of stochastic thermodynamics. We employ the optimal control theory to study the performance of Brownian heat engines and determine the optimal heat-engine cycles in generic damped situation, which were previously known only in the overdamped and the underdamped limits. These optimal cycles include two isothermal processes, two adiabatic processes, and an extra isochoric relaxation process at the upper stiffness constraint. Our results not only interpolate the optimal cycles between the overdamped and the underdamped limits, but also determine the appropriate friction coefficient of the Brownian heat engine to achieve the maximum power. These findings offer valuable insights for the development of high-performance Brownian heat engines in experimental setups., Comment: 7+17 pages, 3+4 figures, accepted version for Phys. Rev. E

In quantum thermodynamics, the two-projective-measurement (TPM) scheme provides a successful description of stochastic work only in the absence of initial quantum coherence. Extending the quantum work distribution to quasiprobability is a general approach to characterize work fluctuation in the presence of initial coherence. However, among a large number of different definitions, there is no consensus on the most appropriate work quasiprobability. In this article, we list several physically reasonable requirements including the first law of thermodynamics, time-reversal symmetry, positivity of second-order moment, and a support condition for the work distribution. We prove that the only definition that satisfies all these requirements is the Margenau-Hill (MH) quasiprobability of work. In this sense, the MH quasiprobability of work shows its advantages over other definitions. As an illustration, we calculate the MH work distribution of a breathing harmonic oscillator with initial squeezed states and show the convergence to classical work distribution in the classical limit., Comment: 15 pages,1 figure

The stochastic thermodynamics of systems with a few degrees of freedom has been studied extensively so far. We would like to extend the study to systems with more degrees of freedom and even further-continuous fields with infinite degrees of freedom. The simplest case for a continuous stochastic field is the Edwards-Wilkinson elastic manifold. It is an exactly solvable model of which the heat statistics in the relaxation process can be calculated analytically. The cumulants require a cutoff spacing to avoid ultra-violet divergence. The scaling behavior of the heat cumulants with time and the system size as well as the large deviation rate function of the heat statistics in the large size limit is obtained.

In this paper, we introduce a novel implicit neural network for the task of single image super-resolution at arbitrary scale factors. To do this, we represent an image as a decoding function that maps locations in the image along with their associated features to their reciprocal pixel attributes. Since the pixel locations are continuous in this representation, our method can refer to any location in an image of varying resolution. To retrieve an image of a particular resolution, we apply a decoding function to a grid of locations each of which refers to the center of a pixel in the output image. In contrast to other techniques, our dual interactive neural network decouples content and positional features. As a result, we obtain a fully implicit representation of the image that solves the super-resolution problem at (real-valued) elective scales using a single model. We demonstrate the efficacy and flexibility of our approach against the state of the art on publicly available benchmark datasets., Comment: To be published in the 2023 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV)

For driven open systems in contact with multiple heat reservoirs, we find the marginal distributions of work or heat do not satisfy any fluctuation theorem, but only the joint distribution of work and heat satisfies a family of fluctuation theorems. A hierarchical structure of these fluctuation theorems is discovered from microreversibility of the dynamics by adopting a step-by-step coarse-graining procedure in both classical and quantum regimes. Thus, we put all fluctuation theorems concerning work and heat into a unified framework. We also propose a general method to calculate the joint statistics of work and heat in the situation of multiple heat reservoirs via the Feynman-Kac equation. For a classical Brownian particle in contact with multiple heat reservoirs, we verify the validity of the fluctuation theorems for the joint distribution of work and heat., Comment: 16 pages, 5 figures, published version

We analytically calculate the cumulant generating function of energy and particle transport in an open 1D Kitaev chain by utilizing the Keldysh technique. The joint distribution of particle and energy currents obeys different fluctuation relations in different regions of the parameter space as a result of $U$(1) symmetry breaking and energy conservation. We discuss the thermoelectricity of the Kitaev chain as a three terminal system and derive an analytical expression of the maximum work power. The response theory up to the second order is explicitly checked, and the result is consistent with the relations derived from the fluctuation relation., Comment: 14 pages, 7 figures. Comments and suggestions are welcomed

We provide a detailed investigation on the fluctuations of the currents in the discrete model of Feynman's ratchet proposed by Jarzynski and Mazonka in 1999. Two macroscopic currents are identified, with the corresponding affinities determined using Schnakenberg's graph analysis. We also investigate full counting statistics of the two currents and show that fluctuation theorem holds for their joint probability distribution. Moreover, fluctuation-dissipation relation, Onsager reciprocal relation and their nonlinear generalizations are numerically shown to be satisfied in this model.

We introduce a numerical approach to calculate the statistics of work done on 1D quantum lattice systems initially prepared in thermal equilibrium states. This approach is based on two tensor-network techniques: Time Evolving Block Decimation (TEBD) and Minimally Entangled Typical Thermal States (METTS). The former is an efficient algorithm used to simulate the dynamics of 1D quantum lattice systems, while the latter a finite-temperature algorithm for generating a set of typical states representing the Gibbs canonical ensemble. As an illustrative example, we apply this approach to the Ising chain in mixed transverse and longitudinal fields. Under an arbitrary protocol, the moment generating function of the work can be obtained, from which the work moments are numerically calculated and the quantum Jarzynski equality can be tested. Moreover, the numerical approach is also adapted to test the universal quantum work relation involving a functional of an arbitrary observable.

Quantum Brownian motion, described by the Caldeira-Leggett model, brings insights to understand phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of a relaxation process in the quantum Brownian motion model. The analytical result of the characteristic function of heat is obtained at any relaxation time with an arbitrary friction coefficient. By taking the classical limit, such a result approaches the heat distribution of the classical Brownian motion described by the Langevin equation, indicating the quantum-classical correspondence principle for heat distribution. We also demonstrate that the fluctuating heat at any relaxation time satisfies the exchange fluctuation theorem of heat, and its long-time limit reflects complete thermalization of the system. Our research brings justification for the definition of the quantum fluctuating heat via two-point measurements., Comment: 32 pages, 2 figures

We study the universality of work statistics of a system quenched through a quantum critical surface. By using the adiabatic perturbation theory, we obtain the general scaling behavior for all cumulants of work. These results extend the studies of Kibble-Zurek mechanism scaling of work statistics from an isolated quantum critical point to a critical surface. As an example, we study the scaling behavior of work statistics in the two-dimensional (2D) Kitaev honeycomb model featured with a critical line. By utilizing the trace formula for quadratic fermionic Hamiltonian, we obtain the exact characteristic function of work of the 2D Kitaev model at zero temperature. The results confirm our prediction.

Abstract The Curzon-Ahlborn (CA) efficiency, as the efficiency at the maximum power (EMP) of the endoreversible Carnot engine, has a significant impact on finite-time thermodynamics. However, the CA engine model is based on many assumptions. In the past few decades, although a lot of efforts have been made, a microscopic theory of the CA engine is still lacking. By adopting the method of the stochastic differential equation of energy, we formulate a microscopic theory of the CA engine realized with an underdamped Brownian particle in a class of non-harmonic potentials. This theory gives microscopic interpretation of all assumptions made by Curzon and Ahlborn, and thus puts the results about CA engine on a solid foundation. Also, based on this theory, we obtain analytical expressions of the power and the efficiency statistics for the Brownian CA engine. Our research brings new perspectives to experimental studies of finite-time microscopic heat engines featured with fluctuations., Comment: 6+15 pages, 2 figures

State functions play important roles in thermodynamics. Different from the process function, such as the exchanged heat $\delta Q$ and the applied work $\delta W$, the change of the state function can be expressed as an exact differential. We prove here that, for a generic thermodynamic system, only the inverse of the temperature, namely $1/T$, can serve as the integration factor for the exchanged heat $\delta Q$. The uniqueness of the integration factor invalidates any attempt to define other state functions associated with the exchanged heat, and in turn, reveals the incorrectness of defining the entransy $E_{vh}=C_VT^2 /2$ as a state function by treating $T$ as an integration factor. We further show the errors in the derivation of entransy by treating the heat capacity $C_V$ as a temperature-independent constant., Comment: 10 pages, 1 figure, has been accepted by Fundamental Research and will be published soon. Comments are welcome

Exchange fluctuation theorems (XFTs) describe a fundamental symmetry relation for particle and energy exchange between several systems. Here we study the XFTs of a Kitaev chain connected to two reservoirs in the same temperature but different bias. By varying the parameters in the Kitaev chain model, we calculate analytically the full counting statistics of the transport current and formulate the corresponding XFTs for multiple current components. We also demonstrate the XFTs with numerical results. We find that due to the presence of the U(1) symmetry breaking terms in the Hamiltonian of the Kitaev chain, various forms of the XFTs emerge, and they can be interpreted in terms of various well-known transport processes.

Quantum Brownian motion model is a typical model in the study of nonequilibrium quantum thermodynamics. Entropy is one of the most fundamental physical concepts in thermodynamics. In this work, by solving the quantum Langevin equation, we study the von Neumann entropy of a particle undergoing quantum Brownian motion. In both the strong and the weak coupling regimes, we obtain the analytical expression of the time evolution of the Wigner function in terms of the initial Wigner function. The result is applied to the thermodynamic equilibrium initial state, which reproduces its classical counterpart in the high-temperature limit. Based on these results, for those initial states having well-defined classical counterparts, we obtain the explicit expression of the quantum corrections to the entropy of the system. Moreover, under the Markovian approximation, we obtain the expression of the quantum corrections to the total entropy production rate ${e_{\rm p}}$ and the heat dissipation rate ${h_{\rm d}}$. Our results bring important insights to the understanding of entropy in open quantum systems.

We investigate the statistics of the work performed during a quench across a quantum phase transition using the adiabatic perturbation theory. It is shown that all the cumulants of work exhibit universal scaling behavior analogous to the Kibble-Zurek scaling for the average density of defects. Two kinds of transformations are considered: quenches between two gapped phases in which a critical point is traversed, and quenches that end near the critical point. In contrast to the scaling behavior of the density of defects, the scaling behavior of the work cumulants are shown to be qualitatively different for these two kinds of quenches. However, in both cases the corresponding exponents are fully determined by the dimension of the system and the critical exponents of the transition, as in the traditional Kibble-Zurek mechanism (KZM). Thus, our study deepens our understanding about the nonequilibrium dynamics of a quantum phase transition by revealing the imprint of the KZM on the work statistics.

The calculation of work distributions in a quantum many-body system is of significant importance and also of formidable difficulty in the field of nonequilibrium quantum statistical mechanics. To solve this problem, inspired by Schwinger-Keldysh formalism, we propose the contour-integral formulation of the work statistics. Based on this contour integral, we show how to do the perturbation expansion of the characteristic function of work (CFW) and obtain the approximate expression of the CFW to the second order of the work parameter for an arbitrary system under a perturbative protocol. We also demonstrate the validity of fluctuation theorems by utilizing the Kubo-Martin-Schwinger condition. Finally, we use noninteracting identical particles in a forced harmonic potential as an example to demonstrate the powerfulness of our approach., Comment: 6 pages, 1 figure

Usually the calculation of work distributions in an arbitrary nonequilibrium process in a quantum system, especially in a quantum many-body system is extremely cumbersome. For all quantum systems described by quadratic Hamiltonians, we invent a universal method for solving the work distribution of quantum systems in an arbitrary driving process by utilizing the group-representation theory. This method enables us to efficiently calculate work distributions where previous methods fail. In some specific models, such as the time-dependent harmonic oscillator, the dynamical Casimir effect, and the transverse XY model, the exact and analytical solutions of work distributions in an arbitrary nonequilibrium process are obtained. Our work initiates the study of quantum stochastic thermodynamics based on group-representation theory.

Work statistics characterizes important features of a non-equilibrium thermodynamic process. But the calculation of the work statistics in an arbitrary non-equilibrium process is usually a cumbersome task. In this work, we study the work statistics in quantum systems by employing Feynman's path-integral approach. We derive the analytical work distributions of two prototype quantum systems. The results are proved to be equivalent to the results obtained based on Schr\"{o}dinger's formalism. We also calculate the work distributions in their classical counterparts by employing the path-integral approach. Our study demonstrates the effectiveness of the path-integral approach to the calculation of work statistics in both quantum and classical thermodynamics, and brings important insights to the understanding of the trajectory work in quantum systems.

The standard definition of quantum fluctuating work is based on the two-projective energy measurement, which however does not apply to systems with initial quantum coherence because the first projective energy measurement destroys the initial coherence, and affects the subsequent evolution of the system. To address this issue, several alternative definitions, such as those based on the full counting statistics and the Margenau-Hill distribution, have been proposed recently. These definitions seem ad hoc because justifications for them are still lacking. In the current study, by utilizing the quantum Feynman-Kac formula and the phase space formulation of quantum mechanics, we prove that the leading order of work distributions is equal to the classical work distribution. Thus we prove the validity of the quantum-classical correspondence of work distributions for initial states with quantum coherence, and provide some justification for those definitions of work. We use an exactly solvable model of the linearly dragged harmonic oscillator to demonstrate our main results., Comment: 12 pages, 1 figure

We study the joint probability distribution function of the work and the change of photon number of the nonequilibrium process of driving the electromagnetic (EM) field in a three-dimensional cavity with an oscillating boundary. The system is initially prepared in a grand canonical equilibrium state and we obtain the analytical expressions of the characteristic functions of work distributions in the single-resonance and multiple-resonance conditions. Our study demonstrates the validity of the fluctuation theorems of the grand canonical ensemble in nonequilibrium processes with particle creation and annihilation. In addition, our work illustrates that in the high temperature limit, the work done on the quantized EM field approaches its classical counterpart; while in the low temperature limit, similar to Casimir effect, it differs significantly from its classical counterpart., Comment: 14 pages, 3 figures

Stochastic thermodynamics provides an important framework to explore small physical systems where thermal fluctuations are inevitable. In the studies of stochastic thermodynamics, some thermodynamic quantities, such as the trajectory work, associated with the complete Langevin equation (the Kramers equation) are often assumed to converge to those associated with the overdamped Langevin equation (the Smoluchowski equation) in the overdamped limit under the overdamped approximation. Nevertheless, a rigorous mathematical proof of the convergence of the work distributions to our knowledge has not been reported so far. Here we study the convergence of the work distributions explicitly. In the overdamped limit, we rigorously prove the convergence of the extended Fokker-Planck equations including work using a multiple timescale expansion approach. By taking the linearly dragged harmonic oscillator as an exactly solvable example, we analytically calculate the work distribution associated with the Kramers equation, and verify its convergence to that associated with the Smoluchowski equation in the overdamped limit. We quantify the accuracy of the overdamped approximation as a function of the damping coefficient. In addition, we experimentally demonstrate that the data of the work distribution of a levitated silica nanosphere agrees with the overdamped approximation in the overdamped limit, but deviates from the overdamped approximation in the low-damping case. Our work fills a gap between the stochastic thermodynamics based on the complete Langevin equation (the Kramers equation) and the overdamped Langevin equation (the Smoluchowski equation), and deepens our understanding of the overdamped approximation in stochastic thermodynamics., Comment: 15 pages, 6 figures

We examine the effects of the Dzyaloshinsky-Moriya (DM) interaction on the nonequilibrium thermodynamics in an anisotropic $XY$ spin chain, which is driven out of equilibrium by a sudden quench of the control parameter of the Hamiltonian. By analytically evaluating the statistical properties of the work distribution and the irreversible entropy production, we investigate the influences of the DM interaction on the nonequilibrium thermodynamics of the system with different parameters at various temperatures. We find that depending on the anisotropy of the system and the temperature, the DM interaction may have different impacts on the nonequilibrium thermodynamics. Interestingly, the critical line induced by the DM interaction can be revealed via the properties of the nonequilibrium thermodynamics. In addition, our results suggest that the strength of the DM interaction can be detected experimentally by studying the nonequilibrium thermodynamics., Comment: 9 pages, 7 figures

We study the heat statistics of a quantum Brownian motion described by the Caldeira-Leggett model. By using the path integral approach, we introduce a novel concept of the quantum heat functional along every pair of Feynman paths. This approach has an advantage of improving our understanding about heat in quantum systems. First, we demonstrate the microscopic reversibility of the system by connecting the heat functional to the forward and its time-reversed probabilities. Second, we analytically prove the quantum-classical correspondence of the heat functional and their statistics, which allows us to obtain better intuitions about the difference between classical and quantum heat., Comment: 11 pages, 1 figure

We investigate quantum corrections to the classical work characteristic function (CF) as a semiclassical approximation to the full quantum work CF. In addition to explicitly establishing the quantum-classical correspondence of the Feynman-Kac formula, we find that these quantum corrections must be in even powers of $\hbar$. Exact formulas of the lowest corrections ($\hbar^2$) are proposed, and their physical origins are clarified. We calculate the work CFs for a forced harmonic oscillator and a forced quartic oscillator respectively to illustrate our results., Comment: Phys.Rev.E, in press