Superstatistics and temperature fluctuations

Generalized thermodynamics or extended irreversible thermodynamics presumes the existence of thermodynamic intensive variables (e.g., temperature, pressure, chemical potentials, generalized potentials) even if the system is removed from equilibrium. It is necessary to properly understand the nature of such intensive variables and, in particular, of their fluctuations, that is, their deviations from those defined in the extended irreversible thermodynamic sense. The meaning of temperature is examined by means of a kinetic theory of macroscopic irreversible processes to assess the validity of the generalized (or extended) thermodynamic method applied to nonequilibrium phenomena. The Boltzmann equation is used for the purpose. Since the relative Boltzmann entropy has been known to be intimately related to the evolution of the aforementioned fluctuations in the intensive thermodynamic variables, we derive the evolution equations for such fluctuations of intensive variables to lay the foundation for investigating the physical implications and evolution of the relative Boltzmann entropy, so that the range of validity of the thermodynamic theory of irreversible processes can be elucidated. Within the framework of this work, we examine a special case of the evolution equations for the aforementioned fluctuations of intensive variables, which also facilitate investigation of the molecular theory meaning of the zeroth law of thermodynamics. We derive an evolution equation describing the relaxation of temperature fluctuations from its local value and present a formula for the temperature relaxation time.

Spatiotemporal pattern of phenology across geographic gradients in insects

Temperature is a fundamental concept in thermodynamics. In macroscopic thermodynamics, systems possess their own intrinsic temperature which equals the reservoir temperature when they equilibrate. In stochastic thermodynamics for simple systems at the microscopic level, thermodynamic quantities other than temperature (a deterministic parameter of the reservoir) are stochastic. To bridge the disparity in the perspectives about temperature between the micro- and macroregimes, we assign a generic mesoscopic N-body system an intrinsic fluctuating temperature T in this work. We simplify the complicated dynamics of numerous particles to one stochastic differential equationwith respect to T, where the noise term accounts for finite-size effects arising from random energy transfer between the system and the reservoir. Our analysis reveals that these fluctuations make the extensive quantities (in the thermodynamic limit) deviate from being extensive. Moreover, we derive finite-size corrections, characterized by heat capacity of the system, to the Jarzynski equality. A possible violation of the principle of maximum work that scales with N^{-1} is also discussed. Additionally, we examine the impact of temperature fluctuations in a finite-size Carnot engine. We show that irreversible entropy production resulting from the temperature fluctuations of the working substance diminishes the average efficiency of the cycle as η_{C}-〈η〉∼N^{-1}, highlighting the unattainability of the Carnot efficiency η_{C} for mesoscopic heat engines even under the quasistatic limit. Our general framework paves the way for further exploration of nonequilibrium thermodynamics and the corresponding finite-size effects in a mesoscopic regime.

The present study investigated and compared the results of establishing composite scores based on the five weighting schemes of the equally-weighted model, the reliability weighting model, the standard deviation (or SD) weighting model, the error of measurement weighting model, and the effective score point model. The purpose of this study was to seek optimal relative weights in forming the best composite possible, as well as to offer more information about the various weighting schemes considered on the different measurement qualities of the tests. The five tests of the Basic Competence Test (BCTEST) were employed for exploration in this research. A random sample of 5,000 examinees drawn from the data obtained from the 2005 test administration was used. To evaluate the various weighting schemes, this study examined the statistical and psychometric properties of the test scores and the weighted composite scores, the effective contributions of individual tests to the composites, as well as the impact on the admission decisions. The findings indicated that the reliability coefficients of the variously formed composite scores were all very high. However, with regard to the effective contributions, the results were very different among the various weighting schemes. Overall, the SD and the error of measurement weighting models seemed to perform better in establishing the composites than the reliability or the effective score point model, although there still remained the issue of inequality of the effective contributions for both the SD and the error of measurement models. Results from this study should advance the understanding of weighting issues while combining individual test components into composites.

Explicit nodal weight functions for a pair of symmetric radial cracks emanating from a hole in a plate are presented with special emphasis on the load-independent characteristics of the explicit weight functions that can obviate repeated calculations of the Mode I stress intensity factors (KI) under different loading conditions. An analytical expression, which relates the explicit crack-face weight function component for Mode I deformation to the radial distance from the crack tip along the crack face, is also provided to facilitate KI evaluation by combining the uncracked stress field and the explicit crack-face weight functions through the use of the linear superposition principle. The utilization of the explicit weight functions, which are obtained from a simple loading, for calculating KI under complex loading conditions such as biaxial loading and pin-joint loading with and without interference pressure, is uniquely demonstrated by combining the superposition principle and the weight function concept.

Understanding the spatial and temporal dynamics of species assemblages is a main challenge in ecology. The mechanisms that shape species assemblages and their temporal fluctuations along tropical elevational gradients are particularly poorly understood. Here, we examined the spatio-temporal dynamics of bird assemblages along an elevational gradient in Ecuador. We conducted bird point counts at three elevations (1000, 2000 and 3000 m) on 18 1-ha plots and repeated the sampling eight times over two years (216 hours in total). For each plot, we obtained data of monthly temperatures and precipitation and recorded the overall resource availability (i.e., the sum of flower, fruit, and invertebrate resources). As expected, bird richness decreased from low to high elevations. Moreover, we found a significant decrease in bird abundance and richness and an increase in evenness between the most and least humid season at each of the three elevations. Climatic factors were more closely related to these temporal fluctuations than local resource availability. While temperature had significant positive effects on the abundance of birds at mid and high elevations, precipitation negatively affected bird abundance at low and mid elevations. Our study highlights that bird assemblages along tropical elevational gradients can show pronounced seasonal fluctuations. In particular, low temperatures and high precipitation seem to impose important constraints on birds. We conclude that potential changes in climate, due to global warming, are likely to affect the spatio-temporal dynamics of bird assemblages along tropical elevational gradients.

Animal behaviour is the overall response to changes in both external environment and internal physiological processes, and investigating the behavioural rhythms of wildlife is essential for understanding the spatio-temporal dynamics of their activities and the factors shaping them. To understand the grouping and activity patterns of sika deer as well as the mechanisms for coexistence among sympatric species, we analysed the camera trapping data in Taohongling National Nature Reserve (TNNR) from 2021 to 2025. In our study, a total of seven distinct grouping patterns were recorded, with 1528 independent observations recorded. From summer to winter, sika deer exhibited a decline in solitary individual activity frequency and showed a greater tendency towards group-based activity, which may be affected significantly by season and breeding cycle. Daily activity patterns differed significantly among seasons (p < .001): in summer, the activity peak occurred at 4.03 am, with an activity level of 0.45, and the nocturnality index reached 91.15% (nocturnal activity). However, with an activity level of 0.57 (95% confidence intervals [CI]: 0.51–0.69), and the nocturnality index was only 61.40% (intermittent nocturnal activity) in winter, indicating a strategy to optimize energy expenditure in response to seasonal fluctuations in temperature and food resources. Most pairs of species showed high levels of overlap in daily activity rhythms (0.68~0.73), while a seasonal decline in spatial overlap between sika deer and other species with similar diets was observed during winter, indicating potential behavioural or ecological segregation. Overall, these insights contribute to unveiling seasonal temporal and spatial distribution patterns as well as grouping behaviour of sika deer, enhancing our understanding of herbivore behavioural adaptations driven by dynamic environmental changes.

The statistical properties of an ultrasonic wave that traverses a medium exhibiting temperature fluctuations are investigated. A heated grid in air is utilized to simulate the random thermal pattern typical of atmospheric and marine environments. The effect of temperature fluctuations on the attenuation of the transmitted pressure field and its mutual coherence is examined.

Chapter 2 - Isolated Systems and Thermal Equilibrium

Large Eddy Simulation (LES) of the lab-scale methane fire plumes investigated experimentally by McCaffrey is performed using the steady laminar flamelet/presumed beta filtered density function model on grids of different resolution ranging from the Taylor length scale to about six times the Kolmogorov length scale. This work focuses on investigating existing subgrid (SGS) mixing models for mixture fraction variance prediction. Three different models based on the local equilibrium assumption, the variance transport equation (VTE) and the second moment transport equation (STE) are assessed. In the non-equilibrium modelling (VTE and STE), the scalar dissipation rate is modelled with an algebraic expression involving an SGS mixing time-scale. The comparison of the solutions is based on the convergence properties of LES statistics for mixture fraction, temperature and axial velocity with respect to the filter width. The simulations show that the equilibrium algebraic model is not suitable for purely buoyant flows. On the other hand, simulations performed with the transport models show that grids coarser than 1 cm cannot resolve adequately the natural laminar instability near the edge of the plume that governs the formation of large-scale vortex and, therefore, underestimate the mixing process, especially in the lower part of the continuous flame. For grid resolutions finer than 1 cm, the STE model is less sensitive to grid refinement than the VTE formulation and differences between the two models are reduced with grid refinement. The STE model predicts also a stronger mixing, resulting in a slightly larger lateral expansion of the fire plume. Predicted solutions by the two models are in quantitative agreement with the experimental data in terms of axial temperature, velocity and temperature fluctuations.

An experimental study of local temperature statistics in turbulent thermal convection is presented. The emissions of plumes and plume clusters are detected by an array of thermistors embedded in the top and bottom plates of a 1 m diameter convection cell. We found that the product STST′ of the temperature skewness ST and the skewness of the temperature time derivative ST′ from the embedded thermistors may be used as a measure of the intensity of plume emissions and that STST′ exhibits a pattern that corresponds well to the orientation of the large-scale circulation in the convecting flow. This is despite the fact that the temperature distribution across the plates is highly uniform, as indicated by the mean temperature of the embedded thermistors. By comparing the spatial distributions of STST′ and of the RMS temperature σ, we further find that the maximum temperature fluctuations take place in regions dominated by plume mixing instead of regions of plume emission. It is also found that temperature fluctuations inside the conducting plates have the same statistical and scaling properties as those in the cell centre.

Within the Maximum Entropy Principle context, the specific heat of the system can be expressed in terms of the extensive variables (mean values) or the intensive variables (Lagrange multipliers). It can be shown that the specific heat of the system represented by a given Hamiltonian is not only a thermodynamical quantity but also a dynamical concept. In this contribution, we analyze the consequences emerging from the dynamical properties of the specific heat whose value can be varied using initial conditions independently of the temperature value for the case of semiquantum nonlinear Hamiltonians. An example is outlined.

Thermodynamic theory of equilibrium fluctuations

The Gibbs canonical distribution, dw ~ exp ( - E( p, q) / kBT ) dp dq, seems one of the most solid pillars of statistical physics. Thermodynamics is believed to be a derivative of this distribution. Since the temperature T is introduced, de facto, from a heat bath by the zeroth law of thermodynamics, this distribution cannot represent a genuine temperature fluctuation; all fluctuations are derived from energy fluctuations ( E ). Increasingly, nanoscale problems are attacked by physics (e.g. glass transition), physical chemistry (e.g. nucleation), or biology (e.g. protein folding). The fluctuations are relatively large because the nano-subsystems are small. The fluctuations should, therefore, completely be collected. The von Laue approach [1 - 3] to subsystem thermodynamics via minimal work for generation of fluctuations also allows the temperature to fluctuate ( T ). For this alternative, statistical physics is a derivative of thermodynamics. Here we show that a decision between the alternatives is possible by a calorimetric determination of the characteristic length of dynamic glass transition in confined geometries.

The internal standard (IS) CE (IS-CE) method is an interesting alternative to other methods for the determination of acidity constants of compounds. Although some of the advantages of this method have been already reported, the method has not been tested yet as regards to temperature effects. This has been the aim of this work, where it is demonstrated that the method can be applied successfully for the determination of pK(a) s at different temperatures, if the acidity constant of the IS at the desired temperature is known. The fact of obtaining the acidity constants at different temperatures allows the calculation of some thermodynamic quantities, such as the molar standard enthalpy and the molar standard entropy in a fast way. It is also demonstrated that if the IS and the test compound have similar standard enthalpy increment, the IS compensates uncontrolled possible temperature fluctuations (e.g., due to Joule heat) inside the capillary obtaining reliable acidity constant values at the desired temperature.