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Herein, a dissipative system tailored for the controlled loading and release of CpG oligodeoxynucleotides (CpG ODNs), known for their pharmacological immunostimulatory properties, is reported. The approach involves multiple cycles of deactivation and activation of the CpG ODNs via its hybridization with a complementary fuel strand, followed by its selective release mediated by the enzymatic activity of T7 exonuclease. The autonomous and temporal behavior of this dissipative system can be tuned by three factors: the design of the fuel strand and its concentration that governs the kinetics of the forward hybridization reaction, as well as the concentration of T7 exonuclease, which regulates the backward energy dissipation reaction. Furthermore, the enzyme's tolerance toward waste accumulation is demonstrated, and the system's robust performance when utilizing various fuel strands in alternating fashion is showcased. The findings underscore the potential of this approach for precise and programmable delivery of therapeutic nucleic acids in multiple cycles, with implications for enhancing immunotherapeutic strategies in which controlled kinetics of the nucleic acid is highly desired. [ABSTRACT FROM AUTHOR]

In recent years, the scalar auxiliary variable based (SAV-based) approach has become very popular and hot in the design of linear, high-order and unconditional energy stable schemes of dissipative systems. However, the nature of SAV-based numerical schemes preserving modified energy dissipation limits its wider application. A relaxation technique to correct the modified energy for the baseline SAV method (RSAV) was proposed by Jiang et al. (J. Comput. Phys. 456:110954, 2022) and general SAV method (R-GSAV) by Zhang and Shen et al. (J. Comput. Phys. 464:111311, 2022). The RSAV/R-GSAV approaches are unconditionally energy stable with respect to a modified energy that is closer to the original free energy when compared with the SAV/GSAV approaches. In this paper, inspired by the RSAV/R-GSAV approaches, we propose a novel technique to correct the modified energy of the SAV/GSAV approaches, which can be proved to be an optimal energy approximation. We construct new high-order implicit-explicit schemes based on the proposed energy-optimized SAV-based (EOP-SAV) approaches. The constructed EOP-SAV schemes not only provide an improved accuracy but also simplify calculation, and can be viewed as the optimal relaxation. We also prove that the numerical schemes based on the EOP-SAV approaches are unconditionally energy stable. Compared with the RSAV approach, the proposed EOP-SAV approaches do not need introduce any relaxed factors and can share the similar procedure for error estimates. Several interesting numerical examples have been presented to demonstrate the accuracy and effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

There are several versions of the damped form of the celebrated Pinney equation, which is the natural partner of the undamped time-dependent harmonic oscillator. In this work, these dissipative versions of the Pinney equation are briefly reviewed. We show that Noether's theorem for the usual time-dependent harmonic oscillator as a guiding principle for derivation of the Pinney equation also works in the damped case, selecting a Noether symmetry-based damped Pinney equation. The results are extended to general nonlinear damped Ermakov systems. A certain time-rescaling always allows to remove the damping from the final equations. [ABSTRACT FROM AUTHOR]

In this paper, by extending some L p -norm inequalities to similar inequalities for Orlicz space ( L Φ -norm), we provide equivalent conditions for composition operators to have the shadowing property on the Orlicz space L Φ (μ) . Additionally, we show that for composition operators on Orlicz spaces, the concepts of generalized hyperbolicity and the shadowing property are equivalent. These results extend similar findings on L p -spaces to Orlicz spaces. [ABSTRACT FROM AUTHOR]

A well‐behaved dynamic library composed of two imines and corresponding amines was subjected to the action of an activated carboxylic acid (ACA), whose decarboxylation is known to be base promoted, in different solvents, namely CD2Cl2, CD3CN, and mixtures of them. Two non‐equilibrium systems are consequently obtained: i) a dissipative (CD2Cl2) and ii) an out‐of‐equilibrium (CD3CN) dynamic library whose composition goes back to equilibrium after a given time. In the former case, the library is fully coupled with the decarboxylation of the ACA, while in the latter, an energy ratchet operates. In the mixed solvents, the library exhibits a mediated behavior. Interestingly, in the presence of an excess of added ACA, the different behavior of the imine library in the two solvents is expected to manifest only when the excess acid is consumed. [ABSTRACT FROM AUTHOR]

Over the last two decades ratchet mechanisms have transformed the understanding and design of stochastic molecular systems—biological, chemical and physical—in a move away from the mechanical macroscopic analogies that dominated thinking regarding molecular dynamics in the 1990s and early 2000s (e.g. pistons, springs, etc), to the more scale‐relevant concepts that underpin out‐of‐equilibrium research in the molecular sciences today. Ratcheting has established molecular nanotechnology as a research frontier for energy transduction and metabolism, and has enabled the reverse engineering of biomolecular machinery, delivering insights into how molecules 'walk' and track‐based synthesisers operate, how the acceleration of chemical reactions enables energy to be transduced by catalysts (both motor proteins and synthetic catalysts), and how dynamic systems can be driven away from equilibrium through catalysis. The recognition of molecular ratchet mechanisms in biology, and their invention in synthetic systems, is proving significant in areas as diverse as supramolecular chemistry, systems chemistry, dynamic covalent chemistry, DNA nanotechnology, polymer and materials science, molecular biology, heterogeneous catalysis, endergonic synthesis, the origin of life, and many other branches of chemical science. Put simply, ratchet mechanisms give chemistry direction. Kinetic asymmetry, the key feature of ratcheting, is the dynamic counterpart of structural asymmetry (i.e. chirality). Given the ubiquity of ratchet mechanisms in endergonic chemical processes in biology, and their significance for behaviour and function from systems to synthesis, it is surely just as fundamentally important. This Review charts the recognition, invention and development of molecular ratchets, focussing particularly on the role for which they were originally envisaged in chemistry, as design elements for molecular machinery. Different kinetically asymmetric systems are compared, and the consequences of their dynamic behaviour discussed. These archetypal examples demonstrate how chemical systems can be driven inexorably away from equilibrium, rather than relax towards it. [ABSTRACT FROM AUTHOR]

Herein, a dissipative system tailored for the controlled loading and release of CpG oligodeoxynucleotides (CpG ODNs), known for their pharmacological immunostimulatory properties, is reported. The approach involves multiple cycles of deactivation and activation of the CpG ODNs via its hybridization with a complementary fuel strand, followed by its selective release mediated by the enzymatic activity of T7 exonuclease. The autonomous and temporal behavior of this dissipative system can be tuned by three factors: the design of the fuel strand and its concentration that governs the kinetics of the forward hybridization reaction, as well as the concentration of T7 exonuclease, which regulates the backward energy dissipation reaction. Furthermore, the enzyme's tolerance toward waste accumulation is demonstrated, and the system's robust performance when utilizing various fuel strands in alternating fashion is showcased. The findings underscore the potential of this approach for precise and programmable delivery of therapeutic nucleic acids in multiple cycles, with implications for enhancing immunotherapeutic strategies in which controlled kinetics of the nucleic acid is highly desired.

This article explores the mechanical analysis of a unified chaotic system and matrix projective synchronization (MPS). The sufficient conditions to achieve MPS of unified chaotic system have derived. The mechanics of unified chaotic system have been examined in contrast with Kolmogorov system, Euler equation, and Hamiltonian function. The Casimir energy function is also introduced to analyze the system dynamics. The unified chaotic system has been transformed into Kolmogorov type system and decomposed into four types of torques: inertial, internal, dissipation, and external torque. In order to view the mechanics behind the unified chaotic system, different particular cases have been discussed. Five scenarios are examined using combinations of various torques in order to identify the key elements in chaos creation and their physical significance. The bifurcation diagram, Lyapunov exponent and Lyapunov dimension validates the generation of chaos for different particular cases [ABSTRACT FROM AUTHOR]

Through duality, it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or right operators. The emergence of these novel fractional integration by parts formulas inspires the introduction of a new calculus of variations, where only one type of fractional derivative (left or right) is present. This applies to both the problem formulation and the corresponding necessary optimality conditions. As a practical application, we present a new Lagrangian that relies solely on left-hand side fractional derivatives. The fractional variational principle derived from this Lagrangian leads us to the equation of motion for a dissipative/damped system. [ABSTRACT FROM AUTHOR]

In this study, the stability problem of a laminated beam with only structural damping is analyzed. The results obtained in this study improve the analysis of the problem by investigating stability without introducing additional dissipation. This is accomplished by considering only the usual assumption of equal wave velocities as the stability criterion. [ABSTRACT FROM AUTHOR]

The use of Activated Carboxylic Acids (ACAs) allows the time‐controlled operation of dissipative chemical systems based on the acid‐base reaction by providing both the stimulus that temporarily drives a physicochemical change and, subsequently, the counter‐stimulus with a single reagent addition. However, their application is inherently limited to acid‐sensitive systems. To overcome this limitation, we herein develop a straightforward device for the transduction of the acid‐base stimuli delivered by an ACA into a voltage signal that, in turn, is used to control voltage‐sensitive circuits that are not pH‐responsive by themselves. The signal transductor can be easily assembled from common laboratory equipment and employs aqueous solutions of readily available chemicals. Furthermore, the operator can simply and intuitively tune the amplitude of the voltage signal, as well as its duration and offset by varying the concentration of the chemical species involved in the transduction process. [ABSTRACT FROM AUTHOR]

A seminumerical approach proposed many years ago for describing gravitational collapse in the post-quasi-static approximation is modified in order to avoid the numerical integration of the basic differential equations the approach is based upon. For doing that we have to impose some restrictions on the fluid distribution. More specifically, we shall assume the vanishing complexity factor condition, which allows for analytical integration of the pertinent differential equations and leads to physically interesting models. Instead, we show that neither the homologous nor the quasi-homologous evolution are acceptable since they lead to geodesic fluids, which are unsuitable for being described in the post-quasi-static approximation. Also, we prove that, within this approximation, adiabatic evolution also leads to geodesic fluids, and therefore, we shall consider exclusively dissipative systems. Besides the vanishing complexity factor condition, additional information is required for a full description of models. We shall propose different strategies for obtaining such an information, which are based on observables quantities (e.g., luminosity and redshift), and/or heuristic mathematical ansatz. To illustrate the method, we present two models. One model is inspired in the well-known Schwarzschild interior solution, and another one is inspired in Tolman VI solution. [ABSTRACT FROM AUTHOR]

There are several versions of the damped form of the celebrated Pinney equation, which is the natural partner of the undamped time-dependent harmonic oscillator. In this work, these dissipative versions of the Pinney equation are briefly reviewed. We show that Noether’s theorem for the usual time-dependent harmonic oscillator as a guiding principle for derivation of the Pinney equation also works in the damped case, selecting a Noether symmetry-based damped Pinney equation. The results are extended to general nonlinear damped Ermakov systems. A certain time-rescaling always allows to remove the damping from the final equations.

In this paper, by extending some Lp-norm inequalities to similar inequalities for Orlicz space (LΦ-norm), we provide equivalent conditions for composition operators to have the shadowing property on the Orlicz space LΦ(μ). Additionally, we show that for composition operators on Orlicz spaces, the concepts of generalized hyperbolicity and the shadowing property are equivalent. These results extend similar findings on Lp-spaces to Orlicz spaces.

This paper presents a complete analytical development of one of the most frequently used problems, in describing the way in which the energy method is applied on the solution of problems on basic physics and engineering courses. The majority of the classical references do not explain the meaning of finding two solutions when using the principle of conservation of mechanical energy. The classical references just consider the existence of one real solution. The problem corresponds to the displacement of a body on an inclined plane with dry friction, the body moves by the action of gravity and by an initial condition of velocity that is given to it. At the lower end of the inclined plane there is a previously compressed spring, that produces an initial force when the body comes into contact with the spring, it is required to determine the maximum displacement that the body will reach, once it comes into contact with the spring. The use of the Newton equations completes and contributes to explain the meaning of the second solution of the problem, to which corresponds with the real behavior of the system. [ABSTRACT FROM AUTHOR]

In this work, a classical non-conservative system is quantised via canonical quantisation. A systematic approach as to how to obtain the Schrödinger equation for a general dissipative system is proposed. The free particle under linear and cubic dissipation are canonically quantised to obtain wave functions, position–momentum uncertainty relations, average energies and probability densities in each case. The method used is general and can be employed to all dissipative systems. [ABSTRACT FROM AUTHOR]

The present model describes the vibrations of a composite beam consisting of two interconnected beams. One component is a material that exhibits only structural dissipation, while the other is a material subjected to additional frictional dissipation. It is well known that the solutions for laminated Timoshenko beams with one component converge to the equilibrium point at rates that depend on the wave propagation velocity. Here, we show that the solution of the complete system decays with exponential or rational rates when the components share a transmission condition. Proofs of the main results are provided using the multiplier method in the frequency domain. Technically, the main ingredients are inequalities of observability type that serve as “propagators” of asymptotic properties from one component to another. [ABSTRACT FROM AUTHOR]

Originating from nineteenth century physics, the concept of entropy—a measure of disorder, randomness, and/or the dissipation of useful energy—underlay a cosmology where order and complexity were seen as highly improbable phenomena in a universe tending toward chaos and disorganisation. Nearly a century later, theoretical frameworks were developed for understanding the production of entropy as an enabling feature of self-organized complexity in the natural world. These ideas would contribute to establishing connections between the origins, development, and evolution of life and the principles of a thermodynamic universe. For some, they also supplied the conceptual foundations for theorizing about a universal natural tendency driving the development of increasingly complex and ordered systems which amplify processes of entropy production and energy dissipation and dispersal. In this paper I chart a path through the aforementioned ideas and present their relevance in framing a relationship between our technological civilization and the Earth system. I then speculate about the prospect of a technosphere whose constitution and activity are aligned with thermodynamic principles of dissipation and entropy-production, drawing on theoretical biology and recent developments in bioengineering to envision a paradigm where technology becomes living matter itself.

The study of emergent behavior of swarms is of great interest for applied sciences. One of the most fundamental questions for self-organizing swarms is whether the swarms disperse or remain in a spatially cohesive configuration. In the paper we study dissipativity properties and spatial cohesiveness of the swarm of self-propelled particles governed by the model rk=-pk(|rk|)rk-∑mak,mrm, where rk∈Rd, k=1,...,n, and A={ak,m} is a symmetric positive-semidefinie matrix. The self-propulsion term is assumed to be continuously differentiable and to grow faster than 1/z, that is, pk(z)z→∞ as z→∞. We establish that the velocity and acceleration of the particles are ultimately bounded. We show that when ker(A) is trivial, the positions of the particles are also ultimately bounded. For systems with ker(A)≠{0}, we show that, while the system might infinitely drift away from its initial location, the particles remain within a bounded distance from the generalized center of mass of the system, which geometrically coincides with the weighted average of agent positions. The weights are determined by the coefficients of the projection matrix onto ker(A). We also discuss the ultimate boundedness for systems with bounded coupling, including the Morse potential systems, and systems governed by power-law potentials with strong repulsion properties. We show that the former systems are ultimately bounded in the velocity-acceleration domain, whereas the models based on the power-law potentials are not. [ABSTRACT FROM AUTHOR]

Using general fractional calculus (GFC) of the Luchko form and non-holonomic variational equations of Sedov type, generalizations of the standard action principle and first Noether theorem are proposed and proved for non-local (general fractional) non-Lagrangian field theory. The use of the GFC allows us to take into account a wide class of nonlocalities in space and time compared to the usual fractional calculus. The use of non-holonomic variation equations allows us to consider field equations and equations of motion for a wide class of irreversible processes, dissipative and open systems, non-Lagrangian and non-Hamiltonian field theories and systems. In addition, the proposed GF action principle and the GF Noether theorem are generalized to equations containing general fractional integrals (GFI) in addition to general fractional derivatives (GFD). Examples of field equations with GFDs and GFIs are suggested. The energy–momentum tensor, orbital angular-momentum tensor and spin angular-momentum tensor are given for general fractional non-Lagrangian field theories. Examples of application of generalized first Noether's theorem are suggested for scalar end vector fields of non-Lagrangian field theory. [ABSTRACT FROM AUTHOR]

The operation of a dissipative network composed of two or three different crown‐ether receptors and an alkali metal cation can be temporally driven by the use (combined or not) of two orthogonal stimuli of a different nature. More specifically, irradiation with light at a proper wavelength and/or addition of an activated carboxylic acid, are used to modulate the binding capability of the above crown‐ethers towards the metal ion, allowing to control over time the occupancy of the metal cation in the crown‐ether moiety of a given ligand. Thus, application of either or both of the stimuli to an initially equilibrated system, where the metal cation is distributed among the crown‐ether receptors depending on the different affinities, causes a programmable change in the receptor occupancies. Consequently, the system is induced to evolve to one or more out‐of‐equilibrium states with different distributions of the metal cation among the different receptors. When the fuel is exhausted or/and the irradiation interrupted, the system reversibly and autonomously goes back to the initial equilibrium state. Such results may contribute to the achievement of new dissipative systems that, taking advantage of multiple and orthogonal stimuli, are featured with more sophisticated operating mechanisms and time programmability. [ABSTRACT FROM AUTHOR]

A seminumerical approach proposed many years ago for describing gravitational collapse in the post-quasi-static approximation is modified in order to avoid the numerical integration of the basic differential equations the approach is based upon. For doing that we have to impose some restrictions on the fluid distribution. More specifically, we shall assume the vanishing complexity factor condition, which allows for analytical integration of the pertinent differential equations and leads to physically interesting models. Instead, we show that neither the homologous nor the quasi-homologous evolution are acceptable since they lead to geodesic fluids, which are unsuitable for being described in the post-quasi-static approximation. Also, we prove that, within this approximation, adiabatic evolution also leads to geodesic fluids, and therefore, we shall consider exclusively dissipative systems. Besides the vanishing complexity factor condition, additional information is required for a full description of models. We shall propose different strategies for obtaining such an information, which are based on observables quantities (e.g., luminosity and redshift), and/or heuristic mathematical ansatz. To illustrate the method, we present two models. One model is inspired in the well-known Schwarzschild interior solution, and another one is inspired in Tolman VI solution.

We formulate and study a generalized virial theorem for contact Hamiltonian systems. Such systems describe mechanical systems in the presence of simple dissipative forces such as Rayleigh friction, or the vertical motion of a particle falling through a fluid (quadratic drag) under the action of constant gravity. We find a generalized virial theorem for contact Hamiltonian systems which is distinct from that obtained earlier for the symplectic case. The 'contact' generalized virial theorem is shown to reduce to the earlier result on symplectic manifolds as a special case. Various examples of dissipative mechanical systems are discussed. We also formulate a generalized virial theorem in the contact Lagrangian framework. [ABSTRACT FROM AUTHOR]

For Hamiltonian systems with time-dependent potential, the Hamiltonian, and thus the energy, is no longer a constant of motion. However, for such systems as the parametric oscillator, i.e., an oscillator with time-dependent frequency ω(t), still, a dynamical invariant can be found that now has the dimension of action. The question, if such an invariant still exists after the addition of a dissipative friction force is analyzed for the classical as well as for the quantum mechanical case from different perspectives, particularly from that of a complex hydrodynamic formulation of quantum mechanics.

For Hamiltonian systems with time-dependent potential, the Hamiltonian, and thus the energy, is no longer a constant of motion. However, for such systems as the parametric oscillator, i.e., an oscillator with time-dependent frequency ω (t) , still, a dynamical invariant can be found that now has the dimension of action. The question, if such an invariant still exists after the addition of a dissipative friction force is analyzed for the classical as well as for the quantum mechanical case from different perspectives, particularly from that of a complex hydrodynamic formulation of quantum mechanics. [ABSTRACT FROM AUTHOR]

In a Hilbert framework, we introduce a new class of fast continuous dissipative dynamical systems for approximating zeroes of an arbitrary maximally monotone operator. This system originates from some change of variable operated in a continuous Nesterov-like model that is driven by the Yosida regularization of the operator and that involves an asymptotic vanishing damping. The proposed model (based upon the Minty representation of maximally monotone operators) is investigated through a first-order reformulation that amounts to dynamics involving three variables: a couple of two variables that lies in the graph of the considered operator, along with an auxiliary variable. We establish the weak convergence towards zeroes of the operator for two of the trajectories, as well as fast convergence to zero of their velocities. We also prove a fast convergence property to zero for the third trajectory and for its velocity. It turns out that our model offers a new and well-adapted framework for discrete counterparts. Several algorithms are then suggested relative to monotone inclusions. Some of them recover some recently developed inertial proximal algorithms that incorporate a correction term in addition to the classical momentum term. [ABSTRACT FROM AUTHOR]

Generalizing Maxwell's (Maxwell 1867 IV. Phil. Trans. R. Soc. Lond. 157, 49-88 (doi:10.1098/rstl.1867.0004)) classical formula, this paper shows how the dissipation potentials for a dissipative system can be derived from the elastic potential of an elastic system undergoing continual failure and recovery. Hence, stored elastic energy gives way to dissipated elastic energy. This continuum-level response is attributed broadly to dissipative microscopic transitions over a multi-well potential energy landscape of a type studied in several previous works, dating from Prandtl's (Prandtl 1928 Ein Gedankenmodell zur kinetischen Theorie der festen Körper. ZAMM 8, 85-106) model of plasticity. Such transitions are assumed to take place on a characteristic time scale T, with a nonlinear viscous response that becomes a plastic response for T → 0 . We consider both discrete mechanical systems and their continuum mechanical analogues, showing how the Reiner-Rivlin fluid arises from nonlinear isotropic elasticity. A brief discussion is given in the conclusions of the possible extensions to other dissipative processes.

The effect of rapid oscillations, related to large dispersion terms, on the dynamics of dissipative evolution equations is studied for the model examples of the 1D complex Ginzburg-Landau and the Kuramoto-Sivashinsky equations. Three different scenarios of this effect are demonstrated. According to the first scenario, the dissipation mechanism is not affected and the diameter of the global attractor remains uniformly bounded with respect to the very large dispersion coefficient. However, the limit equation, as the dispersion parameter tends to infinity, becomes a gradient system. Therefore, adding the large dispersion term actually suppresses the non-trivial dynamics. According to the second scenario, neither the dissipation mechanism, nor the dynamics are essentially affected by the large dispersion and the limit dynamics remains complicated (chaotic). Finally, it is demonstrated in the third scenario that the dissipation mechanism is completely destroyed by the large dispersion, and that the diameter of the global attractor grows together with the growth of the dispersion parameter.

An old and debated problem in Mechanics concerns the capacity of finite dimensional Lagrangian systems to describe dissipation phenomena. It is true that Helmholtz conditions determine not-always verifiable conditions establishing when a system of n second-order ordinary differential equations in normal form (nODEs) be the Lagrange equations deriving from an n th dimensional Lagrangian. However, it is also true that one could conjecture that, given nODEs it is possible to find a (n + k)th dimensional Lagrangian such that the evolution of suitably chosen n Lagrangian parameters allows for the approximation of the solutions of the nODEs. In fact, while it is well known that the ordinary differential equations (ODEs) usually introduced for describing some dissipation phenomena do not verify Helmholtz conditions, in this paper, we give some preliminary evidence for a positive answer to the conjecture that a dissipative system having n degrees of freedom (DOFs) can be approximated, in a finite time interval and in a suitable norm, by an extended Lagrangian system, having a greater number of DOFs. The theoretical foundation necessary to formulate such a conjecture is here laid and three different examples of extended Lagrangians are shown. Finally, we give some computational results, which encourage to deepen the study of the theoretical aspects of the problem. [ABSTRACT FROM AUTHOR]

In a recent paper, we have shown how in Madelung's hydrodynamic formulation of quantum mechanics, the uncertainties are related to the phase and amplitude of the complex wave function. Now we include a dissipative environment via a nonlinear modified Schrödinger equation. The effect of the environment is described by a complex logarithmic nonlinearity that vanishes on average. Nevertheless, there are various changes in the dynamics of the uncertainties originating from the nonlinear term. Again, this is illustrated explicitly using generalized coherent states as examples. With particular focus on the quantum mechanical contribution to the energy and the uncertainty product, connections can be made with the thermodynamic properties of the environment. [ABSTRACT FROM AUTHOR]

This article applies the thermocontextual interpretation (TCI) to open dissipative systems. TCI is a generalization of the conceptual frameworks underlying mechanics and thermodynamics. It defines exergy with respect to the positive-temperature surroundings as a property of state, and it defines the dissipation and utilization of exergy as functional properties of process. The Second Law of thermodynamics states that an isolated system maximizes its entropy (by dissipating and minimizing its exergy). TCI's Postulate Four generalizes the Second Law for non-isolated systems. A non-isolated system minimizes its exergy, but it can do so either by dissipating exergy or utilizing it. A non-isolated dissipator can utilize exergy either by performing external work on the surroundings or by carrying out the internal work of sustaining other dissipators within a dissipative network. TCI defines a dissipative system's efficiency by the ratio of exergy utilization to exergy input. TCI's Postulate Five (MaxEff), introduced here, states that a system maximizes its efficiency to the extent allowed by the system's kinetics and thermocontextual boundary constraints. Two paths of increasing efficiency lead to higher rates of growth and to higher functional complexity for dissipative networks. These are key features for the origin and evolution of life. [ABSTRACT FROM AUTHOR]

The problem of confirming the correspondence of the dynamics of biophysical processes arising from the incomplete and noisy data obtained during monitoring of the state of bioresources or statistics gathering in a series of laboratory experiments to three behavioral modes of paths of discrete dynamic systems (equilibrium, limiting cycle, or chaos) is considered. It is shown using the examples of real monitoring data and results of laboratory experiments that the data-approximation technique yields a dependence function, which excludes the observed qualitative development of the population process. Attempts to plot regression lines based on the monitoring data for dissipative paths do not yield the necessary information. Known models of biophysics with qualitative changes in the behavior are considered that use characteristics of the reproductive function that cannot be interpreted in terms of the environmental role. The Schwartz derivative depends on the third derivative of the second iteration of the function at the moment of stationary-point stability loss. Criteria for discrete dynamic systems are proposed that can be used to analyze the results of computational simulation from the point of view of biophysical adequacy of occurring nonlinear effects. It is suggested that the rate of population change in the model has a range of negative values and the population reproduction curve has at least two nontrivial stationary points. Consideration of the effect of an aggregated group, arising during invasions, in the action models facilitates an essential interpretation of the behavior of the model path. It is proposed to delimit the nonlinear effects arising in discrete iterative models. In the case of an invasive species that has penetrated into the ecosystem and caused the depletion of its vital resources, a rapid transition to collapse of the new population is possible. Our approach with two-attractor models makes it possible to predict the state of a critically low population of an aggressive intruder. [ABSTRACT FROM AUTHOR]

Using general fractional calculus (GFC) of the Luchko form and non-holonomic variational equations of Sedov type, generalizations of the standard action principle and first Noether theorem are proposed and proved for non-local (general fractional) non-Lagrangian field theory. The use of the GFC allows us to take into account a wide class of nonlocalities in space and time compared to the usual fractional calculus. The use of non-holonomic variation equations allows us to consider field equations and equations of motion for a wide class of irreversible processes, dissipative and open systems, non-Lagrangian and non-Hamiltonian field theories and systems. In addition, the proposed GF action principle and the GF Noether theorem are generalized to equations containing general fractional integrals (GFI) in addition to general fractional derivatives (GFD). Examples of field equations with GFDs and GFIs are suggested. The energy–momentum tensor, orbital angular-momentum tensor and spin angular-momentum tensor are given for general fractional non-Lagrangian field theories. Examples of application of generalized first Noether’s theorem are suggested for scalar end vector fields of non-Lagrangian field theory.

In this paper, we provide sufficient conditions for dissipativity and local asymptotic stability of discrete-time dynamical systems parametrized by deep neural networks. We leverage the representation of neural networks as pointwise affine maps, thus exposing their local linear operators and making them accessible to classical system analytic and design methods. This allows us to “crack open the black box” of the neural dynamical system’s behavior by evaluating their dissipativity, and estimating their stationary points and state-space partitioning. We relate the norms of these local linear operators to the energy stored in the dissipative system with supply rates represented by their aggregate bias terms. Empirically, we analyze the variance in dynamical behavior and eigenvalue spectra of these local linear operators with varying weight factorizations, activation functions, bias terms, and depths.

This Concept is focused on the key features of dissipative dynamic combinatorial chemistry (DDCC). DDCC deals with transient libraries of compounds, maintained out‐of‐equilibrium by the consumption of a fuel, whose composition changes upon the selection pressure of kinetic and/or thermodynamic processes. Concepts and definitions of kinetic and thermodynamic dissipative dynamic libraries ("KDDL" and "TDDL"), are introduced and illustrated by a number of actual cases, thus showing the consistency of the present approach. Such concepts and definitions can help establish a common language for this emerging field, which, in our view, has the potential to become highly relevant to supramolecular chemistry. [ABSTRACT FROM AUTHOR]

This article is dedicated to the investigation of the stabilisation problem of a flexible beam attached to the centre of a rotating disk. We assume that the feedback law contains a nonlinear torque control applied on the disk and nonlinear boundary controls exerted on the beam. Thereafter, it is proved that the proposed controls guarantee the exponential stability of the system under a realistic smallness condition on the angular velocity of the disk and general assumptions on the nonlinear functions governing the controls. We used here the strategy of Lasiecka and Tataru (1993) and Alabau-Boussouira (2005, 2010). This permits to improve the stability result shown in Chentouf and Couchouron (1999) in the sense that, on one hand, we deal with a general form of the nonlinear functions involved in the boundary controls. On the other hand, we manage to weaken the conditions on those functions unlike in Chentouf and Couchouron (1999), where the authors consider a special type of functions that are almost linear. [ABSTRACT FROM AUTHOR]

The chemical reagents used to achieve a predictable and programmable time control of the pH of water solutions are reviewed with the purpose to present a toolbox of instruments to be used when a precise pH vs time profile is needed. These tools are particularly useful in view of the growing interest on dissipative systems, many of which operate in water solutions, under the action of reagents (chemical fuels) that allow for programmed pH evolution. After a brief introduction describing the importance of such tools for the operation of dissipative systems in water, five sections follow, which illustrate the different method used so far to temporally control the pH of a water solution. In particular, time‐programmable pH variations based on: 1) bubbling of gases (CO2, N2, Air), 2) hydrolysis of esters, lactones and sultones, 3) enzymatic and biocatalytic networks, 4) decarboxylation reaction of activated carboxylic acids, and 5) pH‐oscillators are described together with selected examples of application. [ABSTRACT FROM AUTHOR]

Life is a planetary feature that depends on its environment, but it has also strongly shaped the physical conditions on Earth, having created conditions highly suitable for a productive biosphere. Clearly, the second law of thermodynamics must apply to these dynamics as well, but how? What insights can we gain by placing life and its effects on planetary functioning in the context of the second law? In Kleidon (2010), I described a thermodynamic Earth system perspective by placing the functioning of the Earth system in terms of the second law. The Earth system is represented by a planetary hierarchy of energy transformations that are driven predominantly by incoming solar radiation, these transformations are constrained by the second law, but they are also modified by the feedbacks from various dissipative activities. It was then hypothesised that life evolves its dissipative activity to the limits imposed by this hierarchy and evolves feedbacks aimed at pushing these limits to higher levels of dissipative activity. Here I provide an update of this perspective. I first review applications to climate and global climate change to demonstrate its success in predicting magnitudes of physical processes, particularly regarding temperatures, heat redistribution and hydrological cycling. I then focus on the limits to dissipative activity of the biosphere. It would seem that the limitations by thermodynamics act indirectly by imposing limitations associated with transport and material exchange. I substantiate this interpretation and discuss the broader implications for habitability, the emergence and evolution of life, and the contemporary biosphere., Competing Interests: Declaration of competing interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Axel Kleidon reports a relationship with European Geosciences Union that includes: board membership. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Author(s). Published by Elsevier B.V. All rights reserved.)