Boltzmann: the probabilistic interpretation of entropy

Boltzmann’s collective work was a mathemetical tour de force. Building on Clausius and Maxwell, he demonstrated that the distribution of gas phase atoms and molecules follows from probability theory. Atoms and molecules distribute themselves in space and momentum to the most probable distribution. Boltzmann used probability theory to quantify the most probable state and then demonstrated the connection between this state and its entropy. This novel approach, later validated by Sackur–Tetrode, led to the creation of statistical mechanics.

Digital Monument Reconstruction in Architectural Studies: Synthesis of Research on the Previously Unknown Form of the Palace in Łobzów (Cracow) from the Period of the Rule of John III Sobieski

The former palace in Łobzów, which currently houses the Faculty of Architecture of the Cracow University of Technology, has an exceedingly rich architectural history. Since the Middle Ages, it has gone through a series of changes that have significantly altered its form each time. Thanks to modern digital reconstruction technology, it was possible to recreate all of its architectural phases in the form of 3D models on the basis of archaeological studies and the analysis of historical materials. The models were then used to reconstruct the most probable appearance of the building during the period when the Polish king John III Sobieski lived there. Determining the most probable state of the palace’s preservation during King Sobieski’s rule, which had not been investigated thus far, was possible only because of the combining of traditional research methods with modern technology.

Celiac disease associated with beta thalassemia minor, coincidence or not: A case report

Introduction: Celiac disease may be associated with a variety of autoimmune diseases such as glucose intolerance, autoimmune thyroid disorders, Sjogren’s syndrome, and untypically with hematological diseases such as beta-thalassemia minor. The simultaneity of celiac disease and beta-thalassemia minor is extremely rare. Only a few cases with both celiac disease and beta-thalassemia minor have been reported in the corresponding medical literature so far. Since the overall prevalence rate of celiac disease is 1% among the public and it has been estimated that 5% of general population has at least one variant allele of thalassemia mutations, the question arises whether the coexistence of celiac disease and beta-thalassemia minor is just a coincidence or etiologic relation. As they both are immune mediated diseases (IMDs), a link between them is possible. Case report:In this study, a 46-year-old man was reported who was admitted with both beta-thalassemia minor and celiac disease. He was referred with probable malabsorption syndrome, causing an iron deficiency anemia and weight loss. Clinically, he was diagnosed with celiac disease and beta-thalassemia minor, which was confirmed later by a small bowel biopsy and hemoglobin (Hb) electrophoresis. The patient was treated with a gluten free diet and folic acid. Conclusion: Celiac disease should be considered as a probable state in patients with beta-thalassemia minor. The prevalence of celiac disease and beta thalassemia minor is significantly high in many countries. Therefore, patients with thalassemia minor should be screened for celiac disease.

Part I The Elements of Bank Financial Supervision, 5 Bank Capital Requirements

This chapter begins by discussing the three overlapping capital requirements that banks are subject to. The first is the orthodox Basel capital requirement. The second is the Leverage Ratio, which is simply a non-risk-weighted capital requirement. The third is the stress test requirement. This has historically been the largest of the three. Stress testing identifies a particular probable state of the world, estimates the total loss which would occur if that state of the world were to eventuate, and requires capital sufficient to ensure that the bank retains sufficient capital after suffering the projected losses. The remainder of the chapter covers Pillar 2 assessment, capital floor, and capital buffers.

Searching for Cerebrovascular Disease Optimal Treatment Recommendations Applying Partially Observable Markov Decision Processes

Partially observable Markov decision processes (POMDPs) are mathematical models for the planning of action sequences under conditions of uncertainty. Uncertainty in POMDPs is manifested in two ways: uncertainty in the perception of model states and uncertainty in the effects of actions on states. The diagnosis and treatment of cerebral vascular diseases (CVD) present this double condition of uncertainty, so we think that POMDP is the most suitable method to model them. In this paper, we propose a model of CVD that is based on observations obtained from neuroimaging studies such as computed tomography, magnetic resonance and ultrasound. The model is designed as a POMDP because the health status of the patient is not directly observable, and only can be deduced, with some probability, from the observations in the cerebral images. The components of the model (states, observations, actions, etc.) were defined based on specialized literature. A diagnosis of the patient’s health status is made and the most appropriate action for the recovery of health is recommended after introducing the observations when operating the model. Consultation of the probable state of health of the patient and alternative actions is also allowed.

Some Special Instances of Entropy Change

A few particular phenomena are quite difficult to frame into the fundamental equation, nonetheless they can be interpreted to the light of the general idea of statistical mechanics that any system and any overall change tend to the most probable state, i.e., a state that is microscopically equilibrated and then macroscopically stable.

Entropy Increase as Tendency: Drive and Effector

A useful definition of entropy is “a function of the system equilibration, stability, and inertness”, and the tendency to an overall increase of entropy, which is set forth by the second law of thermodynamics, should be meant as “the tendency to the most probable state”, that is, to a state having the highest equilibration, stability, and inertness that the system can reach. The tendency to entropy increase is driven by the probabilistic distributions of matter and energy and it is actualized by particle motion.

Outlines of a Verbal Account of the Thermodynamic Entropy for a Pedagogical Approach

Starting from the observation of spontaneous phenomena, it can be envisioned that, with time, every isolated system tends to settle into the most equilibrated, stable, and inert condition. In the very long term, this is the most probable state of a system. This can be shown to be a universal law, the second law of thermodynamics, defined as “the tendency to the most probable state”. Thereafter, it is intuitive that “a function that measures the equilibration, stability, and inertness of a system” is maximized by the second law. This function is called entropy.