Bild Conception of Scientific Theory Structuring in Classical and Quantum Physics: From Hertz and Boltzmann to Schrödinger and De Broglie

We start with a methodological analysis of the notion of scientific theory and its interrelation with reality. This analysis is based on the works of Helmholtz, Hertz, Boltzmann, and Schrödinger (and reviews of D'Agostino). Following Helmholtz, Hertz established the "Bild conception" for scientific theories. Here, "Bild" ("picture") carries the meaning "model" (mathematical). The main aim of natural sciences is construction of the causal theoretical models (CTMs) of natural phenomena. Hertz claimed that a CTM cannot be designed solely on the basis of observational data; it typically contains hidden quantities. Experimental data can be described by an observational model (OM), often based on the price of acausality. CTM-OM interrelation can be tricky. Schrödinger used the Bild concept to create a CTM for quantum mechanics (QM), and QM was treated as OM. We follow him and suggest a special CTM for QM, so-called prequantum classical statistical field theory (PCSFT). QM can be considered as a PCSFT image, but not as straightforward as in Bell's model with hidden variables. The common interpretation of the violation of the Bell inequality is criticized from the perspective of the two-level structuring of scientific theories. Such critical analysis of von Neumann and Bell no-go theorems for hidden variables was performed already by De Broglie (and Lochak) in the 1970s. The Bild approach is applied to the two-level CTM-OM modeling of Brownian motion: the overdamped regime corresponds to OM. In classical mechanics, CTM=OM; on the one hand, this is very convenient; on the other hand, this exceptional coincidence blurred the general CTM-OM structuring of scientific theories. We briefly discuss ontic-epistemic structuring of scientific theories (Primas-Atmanspacher) and its relation to the Bild concept. Interestingly, Atmanspacher as well as Hertz claim that even classical physical theories should be presented on the basic of two-level structuring.

The theory of transport in helical spin-structure crystals

We study helical structures in spin-spiral single crystals. In the continuum approach for the helicity potential energy the simple electronic band splits into two non-parabolic bands. For low exchange integrals, the lower band is described by a surface with a saddle shape in the direction of the helicity axis. Using the Boltzmann equation with the relaxation due to acoustic phonons, we discover the dependence of the current on the angle between the electric field and helicity axis leading to the both parallel and perpendicular to the electric field components in the electroconductivity. The latter can be interpreted as a planar Hall effect. In addition, we find that the transition rates depend on an electron spin allowing the transition between the bands. The electric conductivities exhibit nonlinear behaviors with respect to chemical potentialµ. We explain this effect as the interference of the band anisotropy, spin conservation, and interband transitions. The proposed theory with the spherical model in the effective mass approximation for conduction electrons can elucidate nonlinear dependencies that can be identified in experiments. We find the excellent agreement between the theoretical and experimental data for parallel resistivity depending on temperature at the phase transition from helical to ferromagnetic state in aMnPsingle crystal. In addition, we predict that the perpendicular resistivity abruptly drops to zero in the ferromagnetic phase.

First Digits' Shannon Entropy

Related to the letters of an alphabet, entropy means the average number of binary digits required for the transmission of one character. Checking tables of statistical data, one finds that, in the first position of the numbers, the digits 1 to 9 occur with different frequencies. Correspondingly, from these probabilities, a value for the Shannon entropy H can be determined as well. Although in many cases, the Newcomb-Benford Law applies, distributions have been found where the 1 in the first position occurs up to more than 40 times as frequently as the 9. In this case, the probability of the occurrence of a particular first digit can be derived from a power function with a negative exponent p > 1. While the entropy of the first digits following an NB distribution amounts to H = 2.88, for other data distributions (diameters of craters on Venus or the weight of fragments of crushed minerals), entropy values of 2.76 and 2.04 bits per digit have been found.

Thermodynamic Consistency of the Cushman Method of Computing the Configurational Entropy of a Landscape Lattice

There has been a recent surge of interest in theory and methods for calculating the entropy of landscape patterns, but relatively little is known about the thermodynamic consistency of these approaches. I posit that for any of these methods to be fully thermodynamically consistent, they must meet three conditions. First, the computed entropies must lie along the theoretical distribution of entropies as a function of total edge length, which Cushman showed was a parabolic function following from the fact that there is a normal distribution of permuted edge lengths, the entropy is the logarithm of the number of microstates in a macrostate, and the logarithm of a normal distribution is a parabolic function. Second, the entropy must increase over time through the period of the random mixing simulation, following the expectation that entropy increases in a closed system. Third, at full mixing, the entropy will fluctuate randomly around the maximum theoretical value, associated with a perfectly random arrangement of the lattice. I evaluated these criteria in a test condition involving a binary, two-class landscape using the Cushman method of directly applying the Boltzmann relation (s = klogW) to permuted landscape configurations and measuring the distribution of total edge length. The results show that the Cushman method directly applying the classical Boltzmann relation is fully consistent with these criteria and therefore fully thermodynamically consistent. I suggest that this method, which is a direct application of the classical and iconic formulation of Boltzmann, has advantages given its direct interpretability, theoretical elegance, and thermodynamic consistency.

Promising Thermoelectric Performance in Two-Dimensional Semiconducting Boron Monolayer

A heavy element is a special character for high thermoelectric performance since it generally guarantees a low lattice thermal conductivity. Here, we unexpectedly found a promising thermoelectric performance in a two-dimensional semiconducting monolayer consisting of a light boron element. Using first-principles combined with the Boltzmann transport theory, we have shown that in contrast to graphene or black phosphorus, the boron monolayer has a low lattice thermal conductivity arising from its complex crystal of hexagonal vacancies. The conduction band with an intrinsic camelback shape leads to the high DOS and a high n-type Seebeck coefficient, while the highly degenerate valence band along with the small hole effective mass contributes to the high p-type power factor. As a result, we obtained the p-type thermoelectric figure of merit up to 0.96 at 300 K, indicating that the boron monolayer is a promising p-type thermoelectric material.

Maxwell's role in turning the concept of model into the methodology of modeling

This is a contribution towards a history and philosophy of modeling in its early stages in electromagnetism. In 1873, James Clerk Maxwell (1831-1879) hinted at the methodology of modeling at the end of his Treatise on Electricity and Magnetism. We focus on Maxwell's impact on physicists who immediately followed him, specifically Oliver Lodge (1851-1940) and George Francis FitzGerald (1851-1901). We begin with the role that the scientific concept of model played in the late nineteenth century, as assessed by Ludwig Boltzmann (1844-1906). We then discuss the role of hypothesis as a methodology, the appeal to (dynamical) illustration, and the way Maxwell applied model and working model in his studies of electromagnetism. We show that for Maxwell these key terms were kept distinct, but Lodge did not maintain these distinctions and, in this regard, FitzGerald followed Lodge. Notwithstanding Lodge's influence, Fitzgerald modified Maxwell's theory based on the mechanical model he designed, thereby implicitly taking the first step towards modeling. This methodology consists in drawing consequences from the (mechanical) model to the (electrodynamic) theory and modifying the latter in light of the functioning of the former. At the core of our argument is the thesis that it was a methodological novelty to move from the concept of model to the methodology of modeling. The introduction of modeling as a new methodology into physics in the late nineteenth century was a major event which deserves proper recognition.

Entropy and the Direction of Time

The paper tries to demonstrate that the process of the increase of entropy does not explain the asymmetry of time itself because it is unable to account for its fundamental asymmetries, that is, the asymmetry of traces (we have traces of the past and no traces of the future), the asymmetry of causation (we have an impact on future events with no possibility of having an impact on the past), and the asymmetry between the fixed past and the open future, To this end, the approaches of Boltzmann, Reichenbach (and his followers), and Albert are analysed. It is argued that we should look for alternative approaches instead of this, namely we should consider a temporally asymmetrical physical theory or seek a source of the asymmetry of time in metaphysics. This second approach may even turn out to be complementary if only we accept that metaphysics can complement scientific research programmes.

Molecules, Information and the Origin of Life: What Is Next?

How life did originate and what is life, in its deepest foundation? The texture of life is known to be held by molecules and their chemical-physical laws, yet a thorough elucidation of the aforementioned questions still stands as a puzzling challenge for science. Focusing solely on molecules and their laws has indirectly consolidated, in the scientific knowledge, a mechanistic (reductionist) perspective of biology and medicine. This occurred throughout the long historical path of experimental science, affecting subsequently the onset of the many theses and speculations about the origin of life and its maintenance. Actually, defining what is life, asks for a novel epistemology, a ground on which living systems’ organization, whose origin is still questioned via chemistry, physics and even philosophy, may provide a new key to focus onto the complex nature of the human being. In this scenario, many issues, such as the role of information and water structure, have been long time neglected from the theoretical basis on the origin of life and marginalized as a kind of scenic backstage. On the contrary, applied science and technology went ahead on considering molecules as the sole leading components in the scenery. Water physics and information dynamics may have a role in living systems much more fundamental than ever expected. Can an organism be simply explained by a mechanistic view of its nature or we need “something else”? Probably, we can earn sound foundations about life by simply changing our prejudicial view about living systems simply as complex, highly ordered machines. In this manuscript we would like to reappraise many fundamental aspects of molecular and chemical biology and reading them through a new paradigm, which includes Prigogine’s dissipative structures and informational dissipation (Shannon dissipation). This would provide readers with insightful clues about how biology and chemistry may be thoroughly revised, referring to new models, such as informational dissipation. We trust they are enabled to address a straightforward contribution in elucidating what life is for science. This overview is not simply a philosophical speculation, but it would like to affect deeply our way to conceive and describe the foundations of organisms’ life, providing intriguing suggestions for readers in the field.

Pushing the Limit of Boltzmann Distribution in Cr3+-Doped CaHfO3 for Cryogenic Thermometry

Luminescence Boltzmann thermometry is one of the most reliable techniques used to locally probe temperature in a contactless mode. However, to date, there is no report on cryogenic thermometers based on the highly sensitive and reliable Boltzmann-based ⁴T₂ → ⁴A₂/²E → ⁴A₂ emission ratio of Cr³⁺. On the basis of structural information of the local HfO₆ octahedral site we demonstrated the potential of the CaHfO₃:Cr³⁺ system by combining deep theoretical and experimental investigation. The material exhibits simultaneous emission from both the ²E and ⁴T₂ excited states, following the Boltzmann law in a cryogenic temperature range of 40-150 K. The promising thermometric performance corroborates the potential of CaHfO₃:Cr³⁺ as a Boltzmann cryothermometer, being characterized by a high relative sensitivity (∼ 2%·K^-1 at 40 K) and exceptional thermal resolution (0.045-0.77 K in the 40-150 K range). Moreover, by exploiting the flexibility of the ⁴T₂-²E energy gap controlled by the crystal field of the local octahedral site, the design proposed herein could be expanded to develop new Cr³⁺-doped cryogenic thermometers.

Prediction of bacterial small RNAs in the RsmA (CsrA) and ToxT pathways: a machine learning approach

BACKGROUND

Small RNAs (sRNAs) constitute an important class of post-transcriptional regulators that control critical cellular processes in bacteria. Recent research using high-throughput transcriptomic approaches has led to a dramatic increase in the discovery of bacterial sRNAs. However, it is generally believed that the currently identified sRNAs constitute a limited subset of the bacterial sRNA repertoire. In several cases, sRNAs belonging to a specific class are already known and the challenge is to identify additional sRNAs belonging to the same class. In such cases, machine-learning approaches can be used to predict novel sRNAs in a given class.

METHODS

In this work, we develop novel bioinformatics approaches that integrate sequence and structure-based features to train machine-learning models for the discovery of bacterial sRNAs. We show that features derived from recurrent structural motifs in the ensemble of low energy secondary structures can distinguish the RNA classes with high accuracy.

RESULTS

We apply this approach to predict new members in two broad classes of bacterial small RNAs: 1) sRNAs that bind to the RNA-binding protein RsmA/CsrA in diverse bacterial species and 2) sRNAs regulated by the master regulator of virulence, ToxT, in Vibrio cholerae.

CONCLUSION

The involvement of sRNAs in bacterial adaptation to changing environments is an increasingly recurring theme in current research in microbiology. It is likely that future research, combining experimental and computational approaches, will discover many more examples of sRNAs as components of critical regulatory pathways in bacteria. We have developed a novel approach for prediction of small RNA regulators in important bacterial pathways. This approach can be applied to specific classes of sRNAs for which several members have been identified and the challenge is to identify additional sRNAs.

Caveat on the Boltzmann distribution function use in biology

Sigmoid semilogarithmic functions with shape of Boltzmann equations, have become extremely popular to describe diverse biological situations. Part of the popularity is due to the easy availability of software which fits Boltzmann functions to data, without much knowledge of the fitting procedure or the statistical properties of the parameters derived from the procedure. The purpose of this paper is to explore the plasticity of the Boltzmann function to fit data, some aspects of the optimization procedure to fit the function to data and how to use this plastic function to differentiate the effect of treatment on data and to attest the statistical significance of treatment effect on the data.

Central limit theorems under special relativity

Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.