Physical Properties Of System Research Articles

Is stochastic thermodynamics the key to understanding the energy costs of computation?

The relationship between the thermodynamic and computational properties of physical systems has been a major theoretical interest since at least the 19th century. It has also become of increasing practical importance over the last half-century as the energetic cost of digital devices has exploded. Importantly, real-world computers obey multiple physical constraints on how they work, which affects their thermodynamic properties. Moreover, many of these constraints apply to both naturally occurring computers, like brains or Eukaryotic cells, and digital systems. Most obviously, all such systems must finish their computation quickly, using as few degrees of freedom as possible. This means that they operate far from thermal equilibrium. Furthermore, many computers, both digital and biological, are modular, hierarchical systems with strong constraints on the connectivity among their subsystems. Yet another example is that to simplify their design, digital computers are required to be periodic processes governed by a global clock. None of these constraints were considered in 20th-century analyses of the thermodynamics of computation. The new field of stochastic thermodynamics provides formal tools for analyzing systems subject to all of these constraints. We argue here that these tools may help us understand at a far deeper level just how the fundamental thermodynamic properties of physical systems are related to the computation they perform.

Reliable deep learning in anomalous diffusion against out-of-distribution dynamics.

Anomalous diffusion plays a crucial rule in understanding molecular-level dynamics by offering valuable insights into molecular interactions, mobility states and the physical properties of systems across both biological and materials sciences. Deep-learning techniques have recently outperformed conventional statistical methods in anomalous diffusion recognition. However, deep-learning networks are typically trained by data with limited distribution, which inevitably fail to recognize unknown diffusion models and misinterpret dynamics when confronted with out-of-distribution (OOD) scenarios. In this work, we present a general framework for evaluating deep-learning-based OOD dynamics-detection methods. We further develop a baseline approach that achieves robust OOD dynamics detection as well as accurate recognition of in-distribution anomalous diffusion. We demonstrate that this method enables a reliable characterization of complex behaviors across a wide range of experimentally diverse systems, including nicotinic acetylcholine receptors in membranes, fluorescent beads in dextran solutions and silver nanoparticles undergoing active endocytosis.

Security Control for a Fuzzy System under Dynamic Protocols and Cyber-Attacks with Engineering Applications

The objective of this study is to design a security control for ensuring the stability of systems, maintaining their state within bounded limits and securing operations. Thus, we enhance the reliability and resilience in control systems for critical infrastructure such as manufacturing, network bandwidth constraints, power grids, and transportation amid increasing cyber-threats. These systems operate as singularly perturbed structures with variables changing at different time scales, leading to complexities such as stiffness and parasitic parameters. To manage these complexities, we integrate type-2 fuzzy logic with Markov jumps in dynamic event-triggered protocols. These protocols handle communications, optimizing network resources and improving security by adjusting triggering thresholds in real-time based on system operational states. Incorporating fractional calculus into control algorithms enhances the modeling of memory properties in physical systems. Numerical studies validate the effectiveness of our proposal, demonstrating a 20% reduction in network load and enhanced stochastic stability under varying conditions and cyber-threats. This innovative proposal enables real-time adaptation to changing conditions and robust handling of uncertainties, setting it apart from traditional control strategies by offering a higher level of reliability and resilience. Our methodology shows potential for broader application in improving critical infrastructure systems.

Testing dynamic correlations and nonlinearity in bivariate time series through information measures and surrogate data analysis.

The increasing availability of time series data depicting the evolution of physical system properties has prompted the development of methods focused on extracting insights into the system behavior over time, discerning whether it stems from deterministic or stochastic dynamical systems. Surrogate data testing plays a crucial role in this process by facilitating robust statistical assessments. This ensures that the observed results are not mere occurrences by chance, but genuinely reflect the inherent characteristics of the underlying system. The initial process involves formulating a null hypothesis, which is tested using surrogate data in cases where assumptions about the underlying distributions are absent. A discriminating statistic is then computed for both the original data and each surrogate data set. Significantly deviating values between the original data and the surrogate data ensemble lead to the rejection of the null hypothesis. In this work, we present various surrogate methods designed to assess specific statistical properties in random processes. Specifically, we introduce methods for evaluating the presence of autodependencies and nonlinear dynamics within individual processes, using Information Storage as a discriminating statistic. Additionally, methods are introduced for detecting coupling and nonlinearities in bivariate processes, employing the Mutual Information Rate for this purpose. The surrogate methods introduced are first tested through simulations involving univariate and bivariate processes exhibiting both linear and nonlinear dynamics. Then, they are applied to physiological time series of Heart Period (RR intervals) and respiratory flow (RESP) variability measured during spontaneous and paced breathing. Simulations demonstrated that the proposed methods effectively identify essential dynamical features of stochastic systems. The real data application showed that paced breathing, at low breathing rate, increases the predictability of the individual dynamics of RR and RESP and dampens nonlinearity in their coupled dynamics.

Exact Inference for Continuous-Time Gaussian Process Dynamics

Many physical systems can be described as a continuous-time dynamical system. In practice, the true system is often unknown and has to be learned from measurement data. Since data is typically collected in discrete time, e.g. by sensors, most methods in Gaussian process (GP) dynamics model learning are trained on one-step ahead predictions. While this scheme is mathematically tempting, it can become problematic in several scenarios, e.g. if measurements are provided at irregularly-sampled time steps or physical system properties have to be conserved. Thus, we aim for a GP model of the true continuous-time dynamics. We tackle this task by leveraging higher-order numerical integrators. These integrators provide the necessary tools to discretize dynamical systems with arbitrary accuracy. However, most higher-order integrators require dynamics evaluations at intermediate time steps, making exact GP inference intractable. In previous work, this problem is often addressed by approximate inference techniques. However, exact GP inference is preferable in many scenarios, e.g. due to its mathematical guarantees. In order to enable direct inference, we propose to leverage multistep and Taylor integrators. We demonstrate how exact inference schemes can be derived for these types of integrators. Further, we derive tailored sampling schemes that allow one to draw consistent dynamics functions from the posterior. The learned model can thus be integrated with arbitrary integrators, just like a standard dynamical system. We show empirically and theoretically that our approach yields an accurate representation of the continuous-time system.

A consistent group-theoretic transformation for the block-diagonalization of structural matrices

Symmetry properties of physical systems may be studied through symmetry groups. In recent times, group theory has found application in the study of various problems in structural mechanics, specifically bifurcation, buckling, kinematics and vibration. Computational simplifications are achieved by decomposing the vector space of the problem into smaller subspaces that are independent of each other. When the basis vectors of a subspace are used as the symmetry-adapted variables of that subspace, a smaller problem (associated with a matrix of smaller dimensions) automatically results. However, the same decomposition may be achieved by first obtaining the structural matrix of the system, and then transforming this into a non-overlapping block-diagonal matrix, each independent block being associated with a subspace of the problem. The advantage of this approach is its greater amenability to computer programming, but it does not always give the correct results unless a very specific procedure is followed. The purpose of this contribution is to present a consistent group-theoretic approach for the block diagonalization of structural matrices.

Fractional investigation of time-dependent mass pendulum

In this paper, we aim to study the dynamical behaviour of the motion for a simple pendulum with a mass decreasing exponentially in time. To examine this interesting system, we firstly obtain the classical Lagrangian and the Euler-Lagrange equation of the motion accordingly. Later, the generalized Lagrangian is constructed via non-integer order derivative operators. The corresponding non-integer Euler-Lagrange equation is derived, and the calculated approximate results are simulated with respect to different non-integer orders. Simulation results show that the motion of the pendulum with time-dependent mass exhibits interesting dynamical behaviours, such as oscillatory and non-oscillatory motions, and the nature of the motion depends on the order of non-integer derivative; they also demonstrate that utilizing the fractional Lagrangian approach yields a model that is both valid and flexible, displaying various properties of the physical system under investigation. This approach provides a significant advantage in understanding complex phenomena, which cannot be achieved through classical Lagrangian methods. Indeed, the system characteristics, such as overshoot, settling time, and peak time, vary in the fractional case by changing the value of α. Also, the classical formulation is recovered by the corresponding fractional model when α tends to 1, while their output specifications are completely different. These successful achievements demonstrate diverse properties of physical systems, enhancing the adaptability and effectiveness of the proposed scheme for modelling complex dynamics.

Galilei-invariant and energy-preserving extensions of Benjamin–Bona–Mahony-type equations

The classical Benjamin–Bona–Mahony equation (BBM equation) models unidirectional propagation of long gravity surface waves of small amplitude. Unlike many other water wave models, it lacks the Galilean invariance, which is an essential property of physical systems. It is shown that by an addition of a higher asymptotic order nonlinear term, this deficiency can be corrected, giving rise to a new Galilei invariant Benjamin–Bona–Mahony equation (iBBM equation). Moreover, further additional higher-order terms can be chosen in a way that the augmented model preserves the energy conservation property along with Hamiltonian and Lagrangian structures. The resulting equation is referred to as energy-preserving Benjamin–Bona–Mahony equation (eBBM).It is shown that both the classical BBM equation and the energy-preserving eBBM equations belong to a one-parameter (α) family that shares essentially the same local and nonlocal symmetries, conservation laws, Hamiltonian, and Lagrangian structures, with the BBM and eBBM equations corresponding to parameter values α=0 and α=1, respectively. Symmetry and conservation law classifications reveal a special case α=1/3, which is shown to correspond to a rescaled version of the celebrated integrable Camassa–Holm (CH) equation. Local symmetries and conservation laws are computed, and numerical solution behaviour is compared for the three BBM-type modes and the CH-equivalent eBBM1/3 model.

Connecting Tikhonov regularization to the maximum entropy method for the analytic continuation of quantum Monte Carlo data

Analytic continuation is an essential step in extracting information about the dynamical properties of physical systems from quantum Monte Carlo (QMC) simulations. Different methods for analytic continuation have been proposed and are still being developed. This paper explores a regularization method based on the repeated application of Tikhonov regularization under the discrepancy principle. The method can be readily implemented in any linear algebra package and gives results surprisingly close to the maximum entropy method (MaxEnt). We analyze the method in detail and demonstrate its connection to MaxEnt. In addition, we provide a straightforward method for estimating the noise level of QMC data, which is helpful for practical applications of the discrepancy principle when the noise level is not known reliably.

Purifying teleportation

Coupling to the environment typically suppresses quantum properties of physical systems via decoherence mechanisms. This is one of the main obstacles in practical implementations of quantum protocols. In this work we show how decoherence effects can be reversed/suppressed during quantum teleportation in a network scenario. Treating the environment quantumly, we show that under a general pure dephasing coupling, performing a second teleportation step can probabilistically reverse the decoherence effects if certain commutativity conditions hold. This effect is purely quantum and most pronounced for qubit systems, where in 25 % of instances the decoherence can be reversed completely. As an example, we show the effect in a physical model of a qubit register coupled to a bosonic bath. We also analyze general d-dimensional systems, identifying all instances of decoherence suppression. Our results are proof-of-concept but we believe will be relevant for the emerging field of quantum networks as teleportation is the key building block of network protocols.

Exploiting Different Symmetries for Trajectory Tracking Control with Application to Quadrotors*

High performance trajectory tracking control of quadrotor vehicles is an important challenge in aerial robotics. Symmetry is a fundamental property of physical systems and offers the potential to provide a tool to design high-performance control algorithms. We propose a design methodology that takes any given symmetry, linearises the associated error in a single set of coordinates, and uses LQR design to obtain a high performance control; an approach we term Equivariant Regulator design. We show that quadrotor vehicles admit several different symmetries: the direct product symmetry, the extended pose symmetry and the pose and velocity symmetry, and show that each symmetry can be used to define a global error. We compare the linearised systems via simulation and find that the extended pose and pose and velocity symmetries outperform the direct product symmetry in the presence of large disturbances. This suggests that choices of equivariant and group affine symmetries have improved linearisation error.

The Role of Quantum Mechanics in Understanding the Phenomenon of Consciousness

The article analyzes the effectiveness of quantum theories of mental experience in relation to two ontological problems - the problem of the existence of consciousness in the material world and the problem of the interaction of consciousness and body. A critical analysis of the quantum theories of consciousness by Penrose-Hameroff, M. Tegmark, G. Stapp, M. Fischer and M.B. Mensky shows that they fail to fully explain how complex physical systems generate mental experience without violating the principle of causal closure of the physical world and the principle of epistemological completeness of physics. Quantum mechanics provides specific processes that are the physical basis of the psyche, but do not explain the phenomenal aspect of subjective reality. Nevertheless, the Heisenberg uncertainty principle gives an understanding of how the interaction of consciousness and body within the scientific picture of the world can be carried out without violating the law of energy conservation. It is shown that the quantum theories of consciousness currently being developed have a predominantly panprotopsychic character, which faces a problem due to the fact that the protomental property of physical systems must be expressed quantitatively and correspond to the value included in the physical equations. As a result, it is concluded that in order to develop quantum theories of consciousness more effectively, it is necessary to give an emergent character, not jumping from the quantum level to the psychic, but explaining the mechanism of the emergence of systemic properties during the sequential transition between different ontological regions of existence, including physical, chemical, biological, neurophysiological and psychic.

Data-driven discovery of dimensionless numbers and governing laws from scarce measurements

Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a highly multi-variable system with incomplete governing equations. This paper introduces a mechanistic data-driven approach that embeds the principle of dimensional invariance into a two-level machine learning scheme to automatically discover dominant dimensionless numbers and governing laws (including scaling laws and differential equations) from scarce measurement data. The proposed methodology, called dimensionless learning, is a physics-based dimension reduction technique. It can reduce high-dimensional parameter spaces to descriptions involving only a few physically interpretable dimensionless parameters, greatly simplifying complex process design and system optimization. We demonstrate the algorithm by solving several challenging engineering problems with noisy experimental measurements (not synthetic data) collected from the literature. Examples include turbulent Rayleigh-Bénard convection, vapor depression dynamics in laser melting of metals, and porosity formation in 3D printing. Lastly, we show that the proposed approach can identify dimensionally homogeneous differential equations with dimensionless number(s) by leveraging sparsity-promoting techniques.

Symmetry analysis of irregular objects

The majority of properties of physical systems and molecules are derived from the character and interaction of their constituent atoms. The symmetry of these interactions provides significant insight into the form and quality of resultant properties such as polarizability, dipole moments, and elasticity. In order to better utilise symmetry as a tool within science, here we introduce four novel methods of symmetry analysis as part of the Irregular Particle Symmetry Analysis software (IPSA). The IPSA software package presents a framework for examining continuous symmetry and group theory under a consistent structure, enabling a unique insight into how the geometric symmetry of atomic structures may be examined and quantified. The methods presented within this paper are practical procedures for characterisation and low-cost additions to existing examinations of materials and molecular properties with a wide range of applications, including areas such as electronic structure estimation, calculation simplification, geometry classification, analysis of dynamics, spectrographic interpretation, and property prediction.

Quantum wake dynamics in Heisenberg antiferromagnetic chains

Traditional spectroscopy, by its very nature, characterizes physical system properties in the momentum and frequency domains. However, the most interesting and potentially practically useful quantum many-body effects emerge from local, short-time correlations. Here, using inelastic neutron scattering and methods of integrability, we experimentally observe and theoretically describe a local, coherent, long-lived, quasiperiodically oscillating magnetic state emerging out of the distillation of propagating excitations following a local quantum quench in a Heisenberg antiferromagnetic chain. This “quantum wake” displays similarities to Floquet states, discrete time crystals and nonlinear Luttinger liquids. We also show how this technique reveals the non-commutativity of spin operators, and is thus a model-agnostic measure of a magnetic system’s “quantumness.”

1D Quantum ring: A Toy Model Describing Noninertial Effects on Electronic States, Persistent Current and Magnetization

Inertial effects can affect several properties of physical systems. In particular, in the context of quantum mechanics, such effects have been studied in diverse contexts. In this paper, starting from the Schr\"{o}dinger equation for a rotating frame, we describe the influence of rotation on the energy levels of a quantum particle constrained to a one-dimensional ring in the presence of a uniform magnetic field. We also investigate how the persistent current and the magnetization in the ring are influenced by temperature and rotating effects.

Quantum advantage in learning from experiments.

Quantum technology promises to revolutionize how we learn about the physical world. An experiment that processes quantum data with a quantum computer could have substantial advantages over conventional experiments in which quantum states are measured and outcomes are processed with a classical computer. We proved that quantum machines could learn from exponentially fewer experiments than the number required by conventional experiments. This exponential advantage is shown for predicting properties of physical systems, performing quantum principal component analysis, and learning about physical dynamics. Furthermore, the quantum resources needed for achieving an exponential advantage are quite modest in some cases. Conducting experiments with 40 superconducting qubits and 1300 quantum gates, we demonstrated that a substantial quantum advantage is possible with today's quantum processors.

The Role of the Second Law of Thermodynamics in Continuum Physics: A Muschik and Ehrentraut Theorem Revisited

In continuum physics, constitutive equations model the material properties of physical systems. In those equations, material symmetry is taken into account by applying suitable representation theorems for symmetric and/or isotropic functions. Such mathematical representations must be in accordance with the second law of thermodynamics, which imposes that, in any thermodynamic process, the entropy production must be nonnegative. This requirement is fulfilled by assigning the constitutive equations in a form that guaranties that second law of thermodynamics is satisfied along arbitrary processes. Such an approach, in practice regards the second law of thermodynamics as a restriction on the constitutive equations, which must guarantee that any solution of the balance laws also satisfy the entropy inequality. This is a useful operative assumption, but not a consequence of general physical laws. Indeed, a different point of view, which regards the second law of thermodynamics as a restriction on the thermodynamic processes, i.e., on the solutions of the system of balance laws, is possible. This is tantamount to assuming that there are solutions of the balance laws that satisfy the entropy inequality, and solutions that do not satisfy it. In order to decide what is the correct approach, Muschik and Ehrentraut in 1996, postulated an amendment to the second law, which makes explicit the evident (but rather hidden) assumption that, in any point of the body, the entropy production is zero if, and only if, this point is a thermodynamic equilibrium. Then they proved that, given the amendment, the second law of thermodynamics is necessarily a restriction on the constitutive equations and not on the thermodynamic processes. In the present paper, we revisit their proof, lighting up some geometric aspects that were hidden in therein. Moreover, we propose an alternative formulation of the second law of thermodynamics, which incorporates the amendment. In this way we make this important result more intuitive and easily accessible to a wider audience.

Phase transitions affected by natural and forceful molecular interconversion.

If a binary liquid mixture, composed of two alternative species with equal amounts, is quenched from a high temperature to a low temperature, below the critical point of demixing, then the mixture will phase separate through a process known as spinodal decomposition. However, if the two alternative species are allowed to interconvert, either naturally (e.g., the equilibrium interconversion of enantiomers) or forcefully (e.g., via an external source of energy or matter), then the process of phase separation may drastically change. In this case, depending on the nature of interconversion, two phenomena could be observed: either phase amplification, the growth of one phase at the expense of another stable phase, or microphase separation, the formation of nongrowing (steady-state) microphase domains. In this work, we phenomenologically generalize the Cahn-Hilliard theory of spinodal decomposition to include the molecular interconversion of species and describe the physical properties of systems undergoing either phase amplification or microphase separation. We apply the developed phenomenology to accurately describe the simulation results of three atomistic models that demonstrate phase amplification and/or microphase separation. We also discuss the application of our approach to phase transitions in polyamorphic liquids. Finally, we describe the effects of fluctuations of the order parameter in the critical region on phase amplification and microphase separation.

Exponential decay of mutual information for Gibbs states of local Hamiltonians

The thermal equilibrium properties of physical systems can be described using Gibbs states. It is therefore of great interest to know when such states allow for an easy description. In particular, this is the case if correlations between distant regions are small. In this work, we consider 1D quantum spin systems with local, finite-range, translation-invariant interactions at any temperature. In this setting, we show that Gibbs states satisfy uniform exponential decay of correlations and, moreover, the mutual information between two regions decays exponentially with their distance, irrespective of the temperature. In order to prove the latter, we show that exponential decay of correlations of the infinite-chain thermal states, exponential uniform clustering and exponential decay of the mutual information are equivalent for 1D quantum spin systems with local, finite-range interactions at any temperature. In particular, Araki's seminal results yields that the three conditions hold in the translation-invariant case. The methods we use are based on the Belavkin-Staszewski relative entropy and on techniques developed by Araki. Moreover, we find that the Gibbs states of the systems we consider are superexponentially close to saturating the data-processing inequality for the Belavkin-Staszewski relative entropy.