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Correction: Oks, E. A Possible Explanation of the Proton Radius Puzzle Based on the Second Flavor of Muonic Hydrogen Atoms. Foundations 2022, 2, 912–917 更正:ok, E.基于第二种介子氢原子的质子半径谜题的可能解释。基金会2022,2,912-917

Foundations Pub Date : 2023-09-04 DOI: 10.3390/foundations3030032

Eugene Oks

引用次数: 0

Foundations of Nonequilibrium Statistical Mechanics in Extended State Space 扩展状态空间中的非平衡统计力学基础

Foundations Pub Date : 2023-08-23 DOI: 10.3390/foundations3030030

P. Gujrati

{"title":"Foundations of Nonequilibrium Statistical Mechanics in Extended State Space","authors":"P. Gujrati","doi":"10.3390/foundations3030030","DOIUrl":"https://doi.org/10.3390/foundations3030030","url":null,"abstract":"The review provides a pedagogical but comprehensive introduction to the foundations of a recently proposed statistical mechanics (μNEQT) of a stable nonequilibrium thermodynamic body, which may be either isolated or interacting. It is an extension of the well-established equilibrium statistical mechanics by considering microstates mk in an extended state space in which macrostates (obtained by ensemble averaging A^) are uniquely specified so they share many properties of stable equilibrium macrostates. The extension requires an appropriate extended state space, three distinct infinitessimals dα=(d,de,di) operating on various quantities q during a process, and the concept of reduction. The mechanical process quantities (no stochasticity) like macrowork are given by A^dαq, but the stochastic quantities C^αq like macroheat emerge from the commutator C^α of dα and A^. Under the very common assumptions of quasi-additivity and quasi-independence, exchange microquantities deqk such as exchange microwork and microheat become nonfluctuating over mk as will be explained, a fact that does not seem to have been appreciated so far in diverse branches of modern statistical thermodynamics (fluctuation theorems, quantum thermodynamics, stochastic thermodynamics, etc.) that all use exchange quantities. In contrast, dqk and diqk are always fluctuating. There is no analog of the first law for a microstate as the latter is a purely mechanical construct. The second law emerges as a consequence of the stability of the system, and cannot be violated unless stability is abandoned. There is also an important thermodynamic identity diQ≡diW≥0 with important physical implications as it generalizes the well-known result of Count Rumford and the Gouy-Stodola theorem of classical thermodynamics. The μNEQT has far-reaching consequences with new results, and presents a new understanding of thermodynamics even of an isolated system at the microstate level, which has been an unsolved problem. We end the review by applying it to three different problems of fundamental interest.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"530 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77696639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Entropy Generation and Control: Criteria to Calculate Flow Optimization in Biological Systems 熵的产生和控制:生物系统中计算流量优化的准则

Foundations Pub Date : 2023-08-22 DOI: 10.3390/foundations3030029

J. Bicudo, Pedro Goes Nogueira-de-Sá, J. Chaui-Berlinck

{"title":"Entropy Generation and Control: Criteria to Calculate Flow Optimization in Biological Systems","authors":"J. Bicudo, Pedro Goes Nogueira-de-Sá, J. Chaui-Berlinck","doi":"10.3390/foundations3030029","DOIUrl":"https://doi.org/10.3390/foundations3030029","url":null,"abstract":"Living beings are composite thermodynamic systems in non-equilibrium conditions. Within this context, there are a number of thermodynamic potential differences (forces) between them and the surroundings, as well as internally. These forces lead to flows, which, ultimately, are essential to life itself, but, at the same time, are associated with entropy generation, i.e., a loss of useful work. The maintenance of homeostatic conditions, the tenet of physiology, demands the regulation of these flows by control of variables. However, due to the very nature of these systems, the regulation of flows and control of variables become entangled in closed loops. Here, we show how to combine entropy generation with respect to a process, and control of parameters (in such a process) in order to create a criterium of optimal ways to regulate changes in flows, the coefficient of flow-entropy (CJσ). We demonstrate the restricted possibility to obtain an increase in flow along with a decrease in entropy generation, and the more general situation of increases in flow along with increases in entropy generation of the process. In this scenario, the CJσ aims to identify the best way to combine the gain in flow and the associated loss of useful work. As an example, we analyze the impact of vaccination effort in the spreading of a contagious disease in a population, showing that the higher the vaccination effort the higher the control over the spreading and the lower the loss of useful work by the society.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82055244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fixed Point Results for Generalized 𝜃-Contraction 广义𝜃-Contraction的不动点结果

Foundations Pub Date : 2023-07-26 DOI: 10.3390/foundations3030028

Umar Ishtiaq, Fahim Ud Din, Khaleel Ahmad, Doha A. Kattan, I. Argyros

引用次数: 0

Gerty Cori, a Life Dedicated to Chemical and Medical Research 格蒂·科里，毕生致力于化学和医学研究

Foundations Pub Date : 2023-07-02 DOI: 10.3390/foundations3030027

Juan Núñez Valdés

引用次数: 0

Editorial for the Special Issue of Foundations “Recent Advances in Fractional Differential Equations and Inclusions” 《基金会》特刊社论《分数阶微分方程及其内含物的最新进展》

Foundations Pub Date : 2023-06-15 DOI: 10.3390/foundations3020025

S. Ntouyas