Narrow Results

We revise the steady vortex surface theory following the recent finding of asymmetric vortex sheets (Migdal, 2021). These surfaces avoid the Kelvin–Helmholtz instability by adjusting their discontinuity and shape. The vorticity collapses to the sheet only in an exceptional case considered long ago by Burgers and Townsend, where it decays as a Gaussian on both sides of the sheet. In generic asymmetric vortex sheets (Shariff, 2021), vorticity leaks to one side or another, making such sheets inadequate for vortex sheet statistics and anomalous dissipation. We conjecture that the vorticity in a turbulent flow collapses on a special kind of surface (confined vortex surface or CVS), satisfying some equations involving the tangent components of the local strain tensor.

The most important qualitative observation is that the inequality needed for this solution’s stability breaks the Euler dynamics’ time reversibility. We interpret this as dynamic irreversibility. We have also represented the enstrophy as a surface integral, conserved in the Navier–Stokes equation in the turbulent limit, with vortex stretching and viscous diffusion terms exactly canceling each other on the CVS surfaces.

We have studied the CVS equations for the cylindrical vortex surface for an arbitrary constant background strain with two different eigenvalues. This equation reduces to a particular version of the stationary Birkhoff–Rott equation for the 2D flow with an extra nonanalytic term. We study some general properties of this equation and reduce its solution to a fixed point of a map on a sphere, guaranteed to exist by the Brouwer theorem.

We continue the study of Confined Vortex Surfaces (CVS) that we introduced in the previous paper. We classify the solutions of the CVS equation and find the analytical formula for the velocity field for arbitrary background strain eigenvalues in the stable region. The vortex surface cross-section has the form of four symmetric hyperbolic sheets with a simple equation $\left|y\right||x{|}^{\mu }=\text{const}$ in each quadrant of the tube cross-section ($xy$ plane).

We use the dilute gas approximation for the vorticity structures in a turbulent flow, assuming their size is much smaller than the mean distance between them. We vindicate this assumption by the scaling laws for the surface shrinking to zero in the extreme turbulent limit. We introduce the Gaussian random background strain for each vortex surface as an accumulation of a large number of small random contributions coming from other surfaces far away. We compute this self-consistent background strain, relating the variance of the strain to the energy dissipation rate.

We find a universal asymmetric distribution for energy dissipation. A new phenomenon is a probability distribution of the shape of the profile of the vortex tube in the $xy$ plane. This phenomenon naturally leads to the “multifractal” scaling of the moments of velocity difference $v(r_1)-v(r_2)$. More precisely, these moments have a nontrivial dependence of $n$, $log\mathrm{\Delta }r$, approximating power laws with effective index $\zeta (n,log\mathrm{\Delta }r)$. We derive some general formulas for the moments containing multidimensional integrals. The rough estimate of resulting moments shows the log–log derivative $\zeta (n,log\mathrm{\Delta }r)$ which is approximately linear in $n$ and slowly depends on $log\mathrm{\Delta }r$. However, the value of effective index is wrong, which leads us to conclude that some other solution of the CVS equations must be found. We argue that the approximate phenomenological relations for these moments suggested in a recent paper by Sreenivasan and Yakhot are consistent with the CVS theory. We reinterpret their renormalization parameter $\alpha \approx 0.95$ in the Bernoulli law $p=-\frac{1}{2}\alpha v^2$ as a probability to find no vortex surface at a random point in space.

For the interacting Feynman propagator ${\mathrm{\Delta }}_{F,\mathrm{\text{int}}}(x,y)$ of scalar electrodynamics, we show that the sign property, $\mathrm{\text{Re}}{i\mathrm{\Delta }}_{F,\mathrm{\text{int}}}\ge 0$, may hinge on the reversibility of time evolution. In contrast, $\mathrm{\text{Im}}{i\mathrm{\Delta }}_{F,\mathrm{\text{int}}}$ is indeterminate. When we switch to reduced dynamics under the weak coupling approximation, the positive semidefinite sign of $\mathrm{\text{Re}}{i\mathrm{\Delta }}_{F,\mathrm{\text{int}}}$ is generally lost, unless we impose severe restrictions on the Kraus operators that govern time evolution. With another approximation, the rotating wave approximation, we may recover the sign by restricting the test functions to exponentials under certain conditions.

Why the classical mechanics and quantum mechanics are reversible while the macroscopic thermodynamic processes are irreversible? Is it because both of the two are different fundamental laws? If yes, what is the difference between them? What is the fundamental equation of nonequilibrium statistical physics? Can it provide a unified framework of statistical physics including nonequilibrium states and equilibrium states? How can we derive rigorously the hydrodynamic equations from microscopic kinetics? Does nonequilibrium entropy obey any evolution equation? What is the form of this equation if it exist? What is the microscopic physical basis of entropy production rate namely the law of entropy increase? Can it be described by a quantitative concise formula? What mechanism is responsible for the processes of approach to equlibrium? How to quantitatively describe it? In this paper we try to solve all these problems from a new fundamental equation of statistical physics in a unified fasion.

The cycle model established here, for which the heat leakage and internal irreversibility are considered, consists of two irreversible non-isentropic adiabatic and two isomagnetic field processes. The working substance is composed of many non-interacting spin systems. Based on quantum master equation of an open system in the Heisenberg picture and semi-group approach, the general performance analysis of quantum refrigeration cycle is performed. Expressions for several important performance parameters, such as the cooling rate, coefficient of performance, rate of entropy production and power input, are derived. By using numerical calculations, the cooling rate as a natural optimization goal for a refrigerator is optimized with respect to external magnetic field. The characteristic curves of the cooling rate, rate of entropy production and power input subject to coefficient of performance are plotted. The optimal regions of the cooling rate, coefficient of the performance (COP) and temperatures of the working substance, are determined.

Recently novel current-driven resonant states characterized by the π-phase kinks were proposed in numerical and analytic studies on THz wave emission from intrinsic Josephson junctions based on the coupled sine-Gordon equation. In these states hysteresis behavior is observed with respect to the application process of current, and such behavior is due to nonlinearity in the Josephson coupling term. Varying the strength of the critical current, there exists a critical strength for the hysteresis behavior in the fundamental mode and at the critical strength the applied current at the emission peak coincides with the critical one, which means breakdown of superconductivity in actual systems. In higher-harmonic modes in the vicinity of the critical current, the strength of hysteresis becomes small and emission can be observed in the reverse process. Such "quasi-reversible" behavior may explain "reversible emission" reported in a recent experiment.

In [C. G. Weaver Found. Phys. 51, 1 (2021)], I showed that Boltzmann’s H-theorem does not face a significant threat from the reversibility paradox. I argue that my defense of the H-theorem against that paradox can be used yet again for the purposes of resolving the recurrence paradox without having to endorse heavy-duty statistical assumptions outside of the hypothesis of molecular chaos. As in [C. G. Weaver Found. Phys. 51, 1 (2021)], lessons from the history and foundations of physics reveal precisely how such resolution is achieved.

In this paper, necessity of creation of mechanics of structured particles is discussed. The way to create this mechanics within the laws of classical mechanics with the use of energy equation is shown. The occurrence of breaking of time symmetry within the mechanics of structured particles is shown, as well as the introduction of concept of entropy in the framework of classical mechanics. The way to create the mechanics of non-equilibrium systems in the thermodynamic approach is shown. It is also shown that the use of hypothesis of holonomic constraints while deriving the canonical Lagrange equation made it impossible to describe irreversible dynamics. The difference between the mechanics of structured particles and the mechanics of material points is discussed. It is also shown that the matter is infinitely divisible according to the laws of classical mechanics.

To examine the hybrid nanomaterial transportation within a permeable region, a numerical approach was applied. The permeable domain was filled with a mixture of water with hybrid nanomaterial (Fe₃O${}_4+$ MWCNT). The wavy below wall experiences uniform flux but the top circular wall maintains at cold temperature. Magnetic field in $x$-direction was applied and non-Darcy formulation was applied for applying permeability effect. Gravity forces help the transportation of hybrid nanomaterial and magnetic forces reduce the speed of nanomaterial. Imposing nanomaterial can decline the irreversibility. For simulation of equations, CVFEM was applied and Bejan and Nu numbers were calculated. Verification test depicts the nice agreement and contours for irreversibility have been presented. By imposing Ha, the Be augments about 4.36% while Nu declines around 13.32%. By selecting greater Da, the Nu intensifies around 8.95% while Be declines about 4.35%. Nu elevates around 93.78% with an augment of Ra while Be drops around 52.75%.

The process of equilibration of a colliding hard-disks system is studied in the framework of classical mechanics. The method consists of dividing the nonequilibrium system into the interacting subsystems; the evolution one of these subsystems is analyzed employing generalized Lagrange and Liouville equations. The subsystem–subsystem interaction force is considered as an evolution parameter. The mechanism by which its system equilibrates is described.

To address the problem of dynamic degradation over a finite-precision platform of chaotic maps and the reversibility of linear chaotic maps, we propose an improved model over GF($2^n$) that is called the nondegenerate m-Dimensional $(m\ge 2)$ Integer-Domain Chaotic Maps (mD-IDCMs). This model incorporates modular exponentiation operation, and is capable of constructing nondegenerate IDCMs of any dimension. Moreover, we prove the irreversibility of mD-IDCM and analyze its chaotic behaviors in terms of positive Lyapunov Exponents (LEs). The results of theoretical analysis show that the proposed mD-IDCM model can obtain the desired positive LEs by appropriately configuring its coefficient matrix. Then, we present two instances, and analyze their LEs, Kolmogorov entropy, Sample entropy, Correlation dimension, and the dynamic analysis indicates that the chaotic map constructed by mD-IDCM has ergodicity within a sufficiently large chaotic range. Finally, we design a Pseudo-Random Number Generator (PRNG) with a key to verify the practicability of the mD-IDCM.

In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e. a complete fracture may be produced by oscillation of small jumps. The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement.

The recent monumental detection of gravitational waves by LIGO, the subsequent detection by the LIGO/VIRGO observatories of a binary neutron star merger seen in the gravitational wave signal $GW170817$, the first photo of the event horizon of the supermassive black hole at the center of Andromeda galaxy released by the EHT telescope and the ongoing experiments on Relativistic Heavy Ion Collisions at the BNL and at the CERN, demonstrate that we are witnessing the second golden era of observational relativistic gravity. These new observational breakthroughs, although in the long run would influence our views regarding this Kosmos, in the short run, they suggest that relativistic dissipative fluids (or magnetofluids) and relativistic continuous media play an important role in astrophysical-and also subnuclear-scales. This realization brings into the frontiers of current research theories of irreversible thermodynamics of relativistic continuous media. Motivated by these considerations, we summarize the progress that has been made in the last few decades in the field of nonequilibrium thermodynamics of relativistic continuous media. For coherence and completeness purposes, we begin with a brief description of the balance laws for classical (Newtonian) continuous media and introduce the classical irreversible thermodynamics (CIT) and point out the role of the local-equilibrium postulate within this theory. Tangentially, we touch the program of rational thermodynamics (RT), the Clausius–Duhem inequality, the theory of constitutive relations and the emergence of the entropy principle in the description of continuous media. We discuss at some length, theories of non equilibrium thermodynamics that sprang out of a fundamental paper written by Müller in 1967, with emphasis on the principles of extended irreversible thermodynamics (EIT) and the rational extended irreversible thermodynamics (REIT). Subsequently, after a brief introduction to the equilibrium thermodynamics of relativistic fluids, we discuss the Israel–Stewart transient (or causal) thermodynamics and its main features. Moreover, we introduce the Liu–Müller–Ruggeri theory describing relativistic fluids. We analyze the structure and compare this theory to the class of dissipative relativistic fluid theories of divergent type developed in the late 1990 by Pennisi, Geroch and Lindblom. As far as theories of nonequilibrium thermodynamics of classical media are concerned, it is fair to state that substantial progress has been made and many predictions of the extended theories have been placed under experimental scrutiny. However, at the relativistic level, the situation is different. Although the efforts aiming to the development of a sensible theory (or theories) of nonequilibrium thermodynamics of relativistic fluids (or continuous media) spans less than a half-century, and even though enormous steps in the right direction have been taken, nevertheless as we shall see in this review, still a successful theory of relativistic dissipation is lacking.

We examine classical Bogoliubov's model of a particle coupled to a heat bath which consists of infinitely many stochastic oscillators. Bogoliubov's result¹ suggests that, in the stochastic limit, the model exhibits convergence to thermodynamical equilibrium. It has recently been shown that the system does attain the equilibrium if the coupling constant is small enough.¹² We show that in the case of the large coupling constant, the distribution function ρ_S (q, p, t) → 0 pointwise as t → ∞. This implies that if there is convergence to equilibrium, then the limit measure has no finite momenta. Besides, the probability to find the particle in any finite domain of phase space tends to zero. This is also true for domains in the coordinate space and in the momentum space.

The paper analyzes strategic behavior in a two-stage environmental choice problem under different information scenarios. Given uncertainty about environmental cost and irreversibility of development, "learning without destroying" emerges from strategic competition when information is endogenous and publicly available. This happens since agents trade off the higher payoff of being the first-mover against the potentially free acquisition of endogenous information without developing their own environmental endowment. We prove that in a 2X2 dynamic environmental game with payoff uncertainty and irreversibility publicly available endogenous information could lead players to destroy less in aggregate terms with respect to the case in which information is exogenous.

Entropy generation ($S_{\mathrm{\text{gen}}}$) is associated with the irreversibility of any thermodynamic system. It provides an indication of lost energy of a system. The main objective of this study is to show a method for calculating entropy generation in the human respiratory tract. In this work, human respiratory tract geometries from two different approaches are considered, first one is based on Hess–Murray theory and the second one is based on Weibel’s experimented result. The entropy generation has been calculated considering duct wall friction along with effect of bifurcation and diffusion. In this study, two different physiological conditions have been contemplated, i.e., at rest and at heavy physiological activities. It has shown that $S_{\mathrm{\text{gen}}}$ of human respiratory is lowest at 23rd level of bifurcation. The outcome of the study reveals that the entropy generation rates per day based on Hess–Murray theory at rest and under heavy physiological activities are $8.42\times 10^{-5}$kJ/K and 0.013kJ/K, whereas the same based on Weibel’s experimented result at rest and under heavy physiological activities are $0.221\times 10^{-3}$kJ/K and 0.05kJ/K, respectively.

The present approach of aging and time irreversibility is a consequence of the theory of functional organization that I have developed and presented over recent years (see e.g., Ref. 11). It is based on the effect of physically small and numerous perturbations known as fluctuations, of structural units on the dynamics of the biological system during its adult life. Being a highly regulated biological system, a simple realistic hypothesis, the time-optimum regulation between the levels of organization, leads to the existence of an internal age for the biological system, and time-irreversibility associated with aging. Thus, although specific genes are controlling aging, time-irreversibility of the system may be shown to be due to the degradation of physiological functions. In other words, I suggest that for a biological system, the nature of time is specific and is an expression of the highly regulated integration. An internal physiological age reflects the irreversible course of a living organism towards death because of the irreversible course of physiological functions towards dysfunction, due to the irreversible changes in the regulatory processes. Following the works of Prigogine and his colleagues in physics, and more generally in the field of non-integrable dynamical systems (theorem of Poincaré–Misra), I have stated this problem in terms of the relationship between the macroscopic irreversibility of the functional organization and the basic mechanisms of regulation at the lowest "microscopic" level, i.e., the molecular, lowest level of organization. The neuron-neuron elementary functional interaction is proposed as an illustration of the method to define aging in the nervous system.

The dynamics of a single qubit randomly colliding with an environment consisting of just two qubits is discussed. It is shown that the system reaches an equilibrium state which coincides with a pure random state of three qubits. Furthermore the time average and the ensemble averages of the quantities used to characterize the approach to equilibrium (purity and tangles) coincide, a signature of ergodic behavior.

A discussion of fundamental aspects of quantum theory is presented, stressing the essential role of “events.”

We present an explicit correspondence between quantum mechanics and the classical theory of irreversible thermodynamics as developed by Onsager, Prigogine et al. Our correspondence maps irreversible Gaussian Markov processes into the semiclassical approximation of quantum mechanics. Quantum-mechanical propagators are mapped into thermodynamical probability distributions. The Feynman path integral also arises naturally in this setup. The fact that quantum mechanics can be translated into thermodynamical language provides additional support for the conjecture that quantum mechanics is not a fundamental theory but rather an emergent phenomenon, i.e. an effective description of some underlying degrees of freedom.