Rate of Entropy Production in Stochastic Mechanical Systems

Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for which the fluctuation-dissipation theorem applies, i.e., return-to-equilibrium processes. Two separate ways for ensembles of such mechanical systems forced by noise to reach equilibrium are examined here. First, a restorative potential and damping can be applied, leading to a classical return-to-equilibrium process wherein energy taken out by damping can balance the energy going in from the noise. Second, the process evolves on a compact configuration space (such as random walks on spheres, torsion angles in chain molecules, and rotational Brownian motion) lead to long-time solutions that are constant over the configuration space, regardless of whether or not damping and random forcing balance. This is a kind of potential-free equilibrium distribution resulting from topological constraints. Inertial and noninertial (kinematic) systems are considered. These systems can consist of unconstrained particles or more complex systems with constraints, such as rigid-bodies or linkages. These more complicated systems evolve on Lie groups and model phenomena such as rotational Brownian motion and nonholonomic robotic systems. In all cases, it is shown that the rate of entropy production is closely related to the appropriate concept of Fisher information matrix of the probability density defined by the Fokker–Planck equation. Classical results from information theory are then repurposed to provide computable bounds on the rate of entropy production in stochastic mechanical systems.

Temperature Affects the Time Required to Discern the Relationship between Primary Production and Export Production in the Ocean

Knowledge of the relationship between net primary production (NPP) and export production (EP) in the ocean is required to estimate how the ocean’s biological pump is likely to respond to climate change effects. Here, we show with a theoretical food web model that the relationship between NPP and EP is obscured by the following phenomena: (1) food web dynamics, which cause EP to be a weighted average of new production (NP) over a previous temperature-dependent time interval that can vary between several weeks at 25 °C to several months at 0 °C and, hence, to be much less temporally variable than NP and (2) the temperature dependence of the resiliency of the food web to perturbations, which causes the return to equilibrium to vary from roughly 50 days at 0 °C to 5–10 days at 25 °C. The implication is that the relationship between NPP and EP can be discerned at tropical and subtropical latitudes if measurements of NPP and EP are averages or climatologies over a timeframe of roughly one month. At high latitudes, however, measurements may need to be averaged over a timeframe of roughly one year because the food webs at high latitudes are very likely far from equilibrium with respect to NPP and EP much of the time, and the model can describe only the average behavior of such physically dynamic systems.

Brief communication: Lower-bound estimates for residence time of energy in the atmospheres of Venus, Mars and Titan

The residence time of energy in a planetary atmosphere, τ, which was recently introduced and computed for the Earth's atmosphere (Osácar et al., 2020), is here extended to the atmospheres of Venus, Mars and Titan. τ is the timescale for the energy transport across the atmosphere. In the cases of Venus, Mars and Titan, these computations are lower bounds due to a lack of some energy data. If the analogy between τ and the solar Kelvin–Helmholtz scale is assumed, then τ would also be the time the atmosphere needs to return to equilibrium after a global thermal perturbation.

Imbalances in Copper or Zinc Concentrations Trigger Further Trace Metal Dyshomeostasis in Amyloid-Beta Producing Caenorhabditis elegans

Alzheimer's Disease (AD), a progressive neurodegenerative disease characterized by the buildup of amyloid-beta (Aβ) plaques, is believed to be a disease of trace metal dyshomeostasis. Amyloid-beta is known to bind with high affinity to trace metals copper and zinc. This binding is believed to cause a conformational change in Aβ, transforming Aβ into a configuration more amenable to forming aggregations. Currently, the impact of Aβ-trace metal binding on trace metal homeostasis and the role of trace metals copper and zinc as deleterious or beneficial in AD remain elusive. Given that Alzheimer's Disease is the sixth leading cause of adult death in the U.S., elucidating the molecular interactions that characterize Alzheimer's Disease pathogenesis will allow for better treatment options. To that end, the model organism C. elegans is used in this study. C. elegans, a transparent nematode whose connectome has been fully established, is an amenable model to study AD phenomena using a multi-layered, interconnected approach. Aβ-producing and non-Aβ-producing C. elegans were individually supplemented with copper and zinc. On day 6 and day 9 after synchronization, the percent of worms paralyzed, concentration of copper, and concentration of zinc were measured in both groups of worms. This study demonstrates that dyshomeostasis of trace metals copper or zinc triggers further trace metal dyshomeostasis in Aβ-producing worms, while dyshomeostasis of copper or zinc triggers a return to equilibrium in non-Aβ-producing worms. This supports the characterization of Alzheimer's Disease as a disease of trace metal dyshomeostasis.

Various choices of source terms for a class of two-fluid two-velocity models

The source terms of the Baer–Nunziato model involve highly non-linear return to equilibrium terms. In order to perform numerical simulations of realistic situations, accounting for this relaxation effects is mandatory. Unfortunately, with the classical forms retained for these source terms in the literature, building efficient, robust and accurate numerical schemes is a tricky task. In this paper, we propose different non-classical forms for these source terms. As for the classical ones, they all agree with the second law of thermodynamics and they are thus associated with a growth of an entropy. The great advantage of some of these new forms of source terms is that they are more linear with respect to the conservative variables. Consequently, this allows to propose more robust, efficient and accurate numerical schemes, in particular when considering fractional step approaches for which source terms and convection terms are solved separately.

The development of Need–Threat Internal Resiliency Theory in COVID-19 crisis utilizing deductive axiomatic approach

Resiliency for older people represents the capacity to return to equilibrium when difficulties arise and was found as integral predictor of their health status. This study aims to develop a theory that attempts to explain the older adults’ resiliency perspectives during crisis and how it has affected their well-being and quality of life as population group. Deductive theory generation using axiomatic approach was adopted resulting to five axioms that served as basis for the generation of three propositions such as: (1) An older person’s health needs have tendencies to develop into a health threat, (2) when the threat is perceived, older persons developed a sense of internal control and adaptation to the changes it creates known as internal resiliency, and (3) internal resiliency can influence the quality of life in old age. The evolved theory suggests that in times of crisis (e.g., COVID-19 pandemic), health needs develop into a health threat that compels older persons to develop internal resiliency in order to preserve their integrity, wellbeing and quality of life. This study widens the nursing perspectives in addressing older persons’ resiliency by the unique condition at which older clients are placed affecting both the pathological nature of the illness as well as the preventive interventions which the society is forced to implement.

Brief Communication: Residence Time of Energy in the Atmospheres of Venus, Earth, Mars and Titan

The concept of residence time of energy in a planetary atmosphere τR, recently introduced and computed for the Earth's atmosphere (Osácar et al., 2020), is here extended to the atmospheres of Venus, Mars and Titan. After a global thermal perturbation, τR is the time scale the atmosphere needs to return to equilibrium. The residence times of energy in the atmospheres of Venus, Earth, Mars and Titan have been computed. In the cases of Venus, Mars and Titan, these are mere lower bounds due to a lack of some energy data.

Are the Indian Ragi Markets Integrated?

The Indian consumers and policymakers recognized finger millet (Ragi) increasingly as a nutritious staple. Karnataka, Uttrakhand, Maharashtra, and Tamil Nadu are the major ragi producing States contributing 90 percent of the Indian Ragi production. Various initiatives in recent years have aimed at promoting agricultural market integration. The present study aimed at testing the integration across the ragi markets in Tamil Nadu. The ADF test was used to assess the stationarity, Johansen cointegration, and the VECM model was used to analyze the long-term cointegration among the markets. Granger causality was used to assess the direction of the flow of information across markets. All the price series were first difference stationary. There existed two cointegration equations depicting the long-term integration across the markets. In the majority of the selected markets, a bidirectional flow of information was observed. Chinthamani and Tumkur markets error correction coefficients were significant, indicating that they will return to equilibrium in the short run by making corrections. Chinthamnai price influenced the Tumkur, Hosur, and Denkanikottai price at one month lag. The Tumkur price was influenced by its one-month lag and Hosur and Vellore one-month lag price. Tumkur and Vellore influence Hosur price by one month lag. The analysis found that Indian ragi markets were integrated in the long run.

Equilibrium and Convergence in Income Distribution: The Case of 28 European Countries in the Recent, Turbulent Past (1995–2019)

The authors developed a political economy equilibrium framework for personal income distribution. In the beginning, they set up a theoretical model which was rooted in status theory. With this concept, one may explain a certain or optimal degree of inequality in society and define a steady state to which inequality can converge. By taking the aggregated Gini coefficient due to a collective decision process, deviations from the steady state due to shocks are allowed. A return to equilibrium is feasible with speed which is compatible with the collective decisionmaking process. The authors then conducted an empirical analysis of personal income distribution in 28 European nations for the period before, during and after the great recession of 2009/2010 and the Euro crisis of 2010/2015 (1995–2019). Not surprisingly, they found inequality convergence in the data. However, the speed of convergence is not the same for all countries.

Heat Losses Caused by the Temporary Influence of Wind in Timber Frame Walls Insulated with Fibrous Materials

The paper presents the results of research concerning three fiber materials—mineral wool, hemp fiber and wood wool—as loose-fill thermal insulation materials. The analysis used the material parameters determined in previous works conducted by the authors, such as thermal conductivity and air permeability in relation to bulk density. These materials exhibit open porosity; thus, convection is an essential phenomenon in the heat transfer process. The paper aimed at conducting thermal simulations of various frame wall variants which were filled with the above-mentioned insulation materials. The simulations were performed with the Control Volume Method using the Delphin 5.8 software. The studies accounted for the effect of wind pressure and the time of its influence on a wall insulated by means of fiber material with a thickness of 150 as well as 250 mm. The simulation enabled us to obtain such data as maximal R-value reduction and time to return to equilibrium after filtration for the analyzed materials. The study proved that heat transfer in these insulations strongly depends on the bulk density, thickness of the insulation and wind pressure. The decrease in R is reduced as the density increases. This results from the decreased air permeability characterizing the material. Wind washing causes lower R reduction than air filtration in all models. The greater the thickness, the longer it takes for the models to return to the equilibrium state following air filtration (and wind washing). This period is comparable for air filtration and wind washing. Hemp fibers were characterized with the strongest susceptibility to air filtration; in the case of wood wool, it was also high, but lower than for hemp fibers, while mineral wool was characterized with the lowest.