Statistical mechanics and thermodynamics: A Maxwellian view

One finds, in Maxwell's writings on thermodynamics and statistical physics, a conception of the nature of these subjects that differs in interesting ways from the way they are usually conceived. In particular, though—in agreement with the currently accepted view—Maxwell maintains that the second law of thermodynamics, as originally conceived, cannot be strictly true, the replacement he proposes is different from the version accepted by most physicists today. The modification of the second law accepted by most physicists is a probabilistic one: although statistical fluctuations will result in occasional spontaneous differences in temperature or pressure, there is no way to predictably and reliably harness these to produce large violations of the original version of the second law. Maxwell advocates a version of the second law that is strictly weaker; the validity of even this probabilistic version is of limited scope, limited to situations in which we are dealing with large numbers of molecules en masse and have no ability to manipulate individual molecules. Connected with this is his conception of the thermodynamic concepts of heat, work, and entropy; on the Maxwellian view, these are concept that must be relativized to the means we have available for gathering information about and manipulating physical systems. The Maxwellian view is one that deserves serious consideration in discussions of the foundation of statistical mechanics. It has relevance for the project of recovering thermodynamics from statistical mechanics because, in such a project, it matters which version of the second law we are trying to recover.     

Bushfire rate-of-spread forecasting: Deterministic and statistical approaches to fire modelling

The three basic modelling approaches used to explain forest fire behaviour are theoretically, laboratory or empirically based. Results of all three approaches are reviewed, but it is noted that only the laboratory- and empirically based models have led to forecasting techniques that are in widespread use. These are the Rothermel model and the McArthur meters, respectively. Field tests designed to test the performance of these operational models were carried out in tropical grasslands. A preliminary analysis indicated that the Rothermel model overpredicted spread rates while the McArthur model underpredicted. To improve the forecast of bushfire rate of spread available to operational firefighting crews it is suggested that a time-variable parameter (TYP) recursive least squares algorithm can be used to assign weights to the respective models, with the weights recursively updated as information on fire-front location becomes available. Results of this methodology when applied to US Grasslands fire experiment data indicate that the quality of the input combined with a priori knowledge of the performance of the candidate models plays an important role in the performance of the TVP algorithm. With high-quality input data, the Rothermel model on its own outperformed the TVP algorithm, but with slightly inferior data both approaches were comparable. Though the use of all available data in a multiple linear regression produces a lower sum of squared errors than the recursive, time-variable weighting approach, or that of any single model, the uncertainties of data input and consequent changes in weighting coefficients during operational conditions suggest the use of the TVP algorithm approach.     

The double transfer of thermodynamics: From physics to chemistry and from Europe to America

The aim of this study is twofold: to explore, first, the influence of the intellectual and social conditions on the transfer of thermodynamics to chemistry and thereby the making of chemical thermodynamics, and second, the way that this knowledge was transferred from Europe to America. Consequently, it is of interest to examine the methodological approaches used by physicists and chemists to transfer thermodynamics to chemistry, to evaluate the potential of this science to offer solutions to existing chemical problems, and to discuss the attitude of the scientific community towards these new ideas. The development of chemical thermodynamics in America followed a different route compared to the European experience. Although it was transferred from Europe, it had distinctive characteristics imposed by a different traditional, intellectual and social milieu. This study focuses on the content of the transferred knowledge to America and the direction that this knowledge assumed by the American scientists. As a paradigm, the chemical thermodynamics of Gilbert Newton Lewis will be considered.     

Quantitative realizations of philosophy of science: William Whewell and statistical methods

In this paper, I examine William Whewell’s (1794–1866) ‘Discoverer’s Induction’, and argue that it supplies a strikingly accurate characterization of the logic behind many statistical methods, exploratory data analysis (EDA) in particular. Such methods are additionally well-suited as a point of evaluation of Whewell’s philosophy since the central techniques of EDA were not invented until after Whewell’s death, and so couldn’t have influenced his views. The fact that the quantitative details of some very general methods designed to suggest hypotheses would so closely resemble Whewell’s views of how theories are formed is, I suggest, a strongly positive comment on his views.     

Equilibrium constant for calcium ion and ascorbate ion

The combination of calcium and ascorbic acid in water at 25 degrees C has been examined by measuring the change of free calcium ion concentration as ascorbate was added in small increment to a solution of calcium. The data show clearly that complex formation between calcium ion and ascorbate ion occurred. At ionic strength mu = 0.1-0.2, the equilibrium constant of Ca++ and the singly-charged ascorbate ion has been measured to be 2.1 M-1. The precision of the result is better than 5% and the accuracy is estimated to be better than 20%. The application of the equilibrium constants is discussed.     

Equilibrium constant for calcium ion and ascorbate ion

Summary The combination of calcium and ascorbic acid in water at 25°C has been examined by measuring the change of free calcium ion concentration as ascorbate was added in small increment to a solution of calcium. The data show clearly that complex formation between calcium ion and ascorbate ion occurred. At ionic strength =0.1–0.2, the equilibrium constant of Ca⁺⁺ and the singly-charged ascorbate ion has been measured to be 2.1 M^–1. The precision of the result is better than 5% and the accuracy is estimated to be better than 20%. The application of the equilibrium constants is discussed.     

Economic and statistical measures of forecast accuracy

This paper argues in favour of a closer link between the decision and the forecast evaluation problems. Although the idea of using decision theory for forecast evaluation appears early in the dynamic stochastic programming literature, and has continued to be used with meteorological forecasts, it is hardly mentioned in standard academic texts on economic forecasting. Some of the main issues involved are illustrated in the context of a two‐state, two‐action decision problem as well as in a more general setting. Relationships between statistical and economic methods of forecast evaluation are discussed and links between the Kuipers score used as a measure of forecast accuracy in the meteorology literature and the market timing tests used in finance are established. An empirical application to the problem of stock market predictability is also provided, and the conditions under which such predictability could be explained in the presence of transaction costs are discussed. Copyright © 2000 John Wiley & Sons, Ltd.     

Going up in flames: necrotic cell injury and inflammatory diseases

Recent evidence indicates that cell death can be induced through multiple mechanisms. Strikingly, the same death signal can often induce apoptotic as well as non-apoptotic cell death. For instance, inhibition of caspases often converts an apoptotic stimulus to one that causes necrosis. Because a dedicated molecular circuitry distinct from that controlling apoptosis is required for necrotic cell injury, terms such as “programmed necrosis” or “necroptosis” have been used to distinguish stimulus-dependent necrosis from those induced by non-specific traumas (e.g., heat shock) or secondary necrosis induced as a consequence of apoptosis. In several experimental models, programmed necrosis/necroptosis has been shown to be a crucial control point for pathogen- or injury-induced inflammation. In this review, we will discuss the molecular mechanisms that regulate programmed necrosis/necroptosis and its biological significance in pathogen infections, drug-induced cell injury, and trauma-induced tissue damage.     

Local Fluctuations and Local Observers in Equilibrium Statistical Mechanics

The distribution function associated with a classical gas at equilibrium is considered. We prove that apart from a factorisable multiplier, the distribution function is fully determined by the correlations among local momenta fluctuations. Using this result we discuss the conditions which enable idealised local observers, who are immersed in the gas and form a part of it, to determine the distribution ‘from within’. This analysis sheds light on two views on thermodynamic equilibrium, the ‘ergodic’ and the ‘thermodynamic limit’ schools, and the relations between them. It also provides an outline for a new definition of equilibrium that is weaker than full ergodicity. Finally, we briefly discuss the possibility that the distribution can be determined by external observers.     

Determination and statistical comparisons of Michaelis-Menten kinetic parameters

Summary A method is described for determining and statistically comparing Michaelis-Menten kinetic parameters.This work was supported in part by a U.S.P.H.S. Grant No. AM 15745 from the National Institute of Arthritis, Metabolism and Digestive Diseases and by the Maine State Agricultural Experiment Station.     

Seasonal pattern of melatonin excretion in humans: relationship to daylength variation rate and geomagnetic field fluctuations

In order to investigate the influence of various environmental parameters on melatonin excretion, the night-time urinary melatonin excretion of 16 healthy volunteers was measured in samples collected monthly over a period of one year. No significant interindividual differences were detected in the monthly rate of change of melatonin excretion. A seasonal bimodal pattern did, however, emerge. Peak values were observed in June and November. In these months a combination of high daylength stability and low values of the vertical component of the geomagnetic field was recorded. Trough values were found in April and August–October when low daylength stability was combined with high values of the vertical component of the geomagnetic field. We propose that the daylength variation rate, and the fluctuations of the vertical component of the geomagnetic field, interact to induce the changes in melatonin secretion which signalize the different seasons in humans.     

Taking times out: Tense logic as a theory of time

Ulrich Meyer’s book The Nature of Time uses tense logic to argue for a ‘modal’ view of time, which replaces substantial times (as in Newton’s Absolute Time) with ‘ersatz times’ constructed using conceptually basic tense operators. He also argues against Bertrand Russell’s relationist theory, in which times are classes of events, and against the idea that relativity compels the integration of time and space (called by Meyer the Inseparability Argument). I find fault with each of these negative arguments, as well as with Meyer’s purported reconstruction of empty spacetime from tense operators and substantial spatial points. I suggest that Meyer’s positive project is best conceived as an elimination of time in the mode of Julian Barbour's The End of Time.     

Proving the principle: Taking geodesic dynamics too seriously in Einstein's theory

In this paper I critically review attempts to formulate and derive the geodesic principle, which claims that free massive bodies follow geodesic paths in general relativity theory. I argue that if the principle is (canonically) interpreted as a law of motion describing the actual evolution of gravitating bodies, then it is impossible to generically apply the law to massive bodies in a way that is coherent with Einstein's field equations. Rejecting the canonical interpretation, I propose an alternative interpretation of the geodesic principle as a type of universality thesis analogous to the universality behavior exhibited in thermal systems during phase transitions.     

Overmathematisation in game theory: pitting the Nash Equilibrium Refinement Programme against the Epistemic Programme

The paper argues that the Nash Equilibrium Refinement Programme was less successful than its competitor, the Epistemic Programme (Interactive Epistemology). The prime criterion of success is the extent to which the programmes were able to reach the key objective guiding non-cooperative game theory for much of the twentieth century, namely, to develop a complete characterisation of the strategic rationality of economic agents in the form of the ultimate solution concept for any normal form and extensive game. The paper explains this in terms of unjustified degrees of mathematisation in Nash Equilibrium Refinement Programme. While this programme’s mathematical models were often inspired by purely mathematical concerns rather than the economic phenomena they were intended to model, the Epistemic Programme’s models were developed with a keen eye to the role beliefs and desires play in strategic interaction between rational economic agents playing games; that is, their interactive epistemology. The Epistemic Programme succeeded in developing mathematical models formalising aspects of strategic interaction that remained implicit in the Nash Equilibrium Refinement Programme (NERP) owing to an unjustified degree of mathematisation. As a result, the Epistemic Programme is the more successful theory.     

A philosophical study of the transition from the caloric theory of heat to thermodynamics: Resisting the pessimistic meta-induction

I began this study with Laudan's argument from the pessimistic induction and I promised to show that the caloric theory of heat cannot be used to support the premisses of the meta-induction on past scientific theories. I tried to show that the laws of experimental calorimetry, adiabatic change and Carnot's theory of the motive power of heat were (i) independent of the assumption that heat is a material substance, (ii) approximately true, (iii) deducible and accounted for within thermodynamics.I stressed that results (i) and (ii) were known to most theorists of the caloric theory and that result (iii) was put forward by the founders of the new thermodynamics. In other words, the truth-content of the caloric theory was located, selected carefully, and preserved by the founders of thermodynamics.However, the reader might think that even if I have succeeded in showing that laudan is wrong about the caloric theory, I have not shown how the strategy followed in this paper can be generalised against the pessimistic meta-induction. I think that the general strategy against Laudan's argument suggested in this paper is this: the empirical success of a mature scientific theory suggests that there are respects and degrees in which this theory is true. The difficulty for — and and real challenge to — philosophers of science is to suggest ways in which this truth-content can be located and shown to be preserved — if at all — to subsequent theories. In particular, the empirical success of a theory does not, automatically, suggest that all theoretical terms of the theory refer. On the contrary, judgments of referential success depend on which theoretical claims are well-supported by the evidence. This is a matter of specific investigation. Generally, one would expect that claims about theoretical entities which are not strongly supported by the evidence or turn out to be independent of the evidence at hand, are not compelling. For simply, if the evidence does not make it likely that our beliefs about putative theoretical entities are approximately correct, a belief in those entities would be ill-founded and unjustified. Theoretical extrapolations in science are indespensable , but they are not arbitrary. If the evidence does not warrant them I do not see why someone should commit herself to them. In a sense, the problem with empricist philisophers is not that they demand that theoretical beliefs must be warranted by evidence. Rather, it is that they claim that no evidence can warrant theorretical beliefs. A realist philosopher of science would not disagree on the first, but she has good grounds to deny the second.I argued that claims about theoretical entities which are not strongly supported by the evidence must not be taken as belief-worthy. But can one sustaon the more ambitious view that loosely supported parts of a theory tend to be just those that include non-referring terms? There is an obvious excess risk in such a generalisation. For there are well-known cases in which a theoretical claim was initially weakly supported by the evidence