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Nonequilibrium thermodynamics as a symplecto-contact reduction and relative information entropy 非平衡热力学作为交联-接触还原和相对信息熵
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2023-12-01 DOI: 10.1016/S0034-4877(23)00084-8
Jin-wook Lim, Yong-Geun Oh
{"title":"Nonequilibrium thermodynamics as a symplecto-contact reduction and relative information entropy","authors":"Jin-wook Lim,&nbsp;Yong-Geun Oh","doi":"10.1016/S0034-4877(23)00084-8","DOIUrl":"10.1016/S0034-4877(23)00084-8","url":null,"abstract":"<div><div>Both statistical phase space (SPS), which is Γ = <em>T</em>*\u0000\t\t\t\t<span><math><mrow><mi>R</mi></mrow></math></span><sup>3<em>N</em></sup> of <em>N</em><span>-body particle system, and kinetic theory phase space (KTPS), which is the cotangent bundle </span><em>T</em>*\u0000\t\t\t\t<span><math><mrow><mi>P</mi></mrow></math></span>(Γ) of the probability space \u0000\t\t\t\t<span><math><mrow><mi>P</mi></mrow></math></span><span><span>(Γ) thereon, carry canonical symplectic structures. Starting from this first principle, we provide a canonical derivation of thermodynamic phase space (TPS) of </span>nonequilibrium thermodynamics<span> as a contact manifold in two steps. First, regarding the collective observation of observables in SPS as a moment map defined on KTPS, we apply the Marsden–Weinstein reduction and obtain a mesoscopic phase space in between KTPS and TPS as a (infinite-dimensional) symplectic fibration. Then we show that the reduced relative information entropy defines a generating function that provides a covariant construction of a thermodynamic equilibrium as a Legen-drian submanifold. This Legendrian submanifold is not necessarily graph-like. We interpret the Maxwell construction of </span></span><em>equal-area law</em><span> as the procedure of finding a continuous, not necessarily differentiable, thermodynamic potential<span> and explain the associated phase transition by identifying the procedure with that of finding a graph selector in symplecto-contact geometry and in the Aubry-Mather theory of dynamical system.</span></span></div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"92 3","pages":"Pages 347-400"},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139061693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A categorical view on the principle of relativity 关于相对论原理的分类观点
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2023-12-01 DOI: 10.1016/S0034-4877(23)00081-2
L.M. Gaio, B.F. Rizzuti
{"title":"A categorical view on the principle of relativity","authors":"L.M. Gaio,&nbsp;B.F. Rizzuti","doi":"10.1016/S0034-4877(23)00081-2","DOIUrl":"10.1016/S0034-4877(23)00081-2","url":null,"abstract":"<div><div>Category theory<span> plays a special role in mathematics — it unifies distinct branches under the same formalism. Despite this integrative power in math, it also seems to provide the proper foundations to the experimental physicist. In this work, we present another application of category in physics, related to the principle of relativity. The operational construction of (inertial) frames of reference indicates that only the movement between one and another frame is enough to differentiate both of them. This fact is hidden when one applies only group theory to connect frames. In fact, rotations and translations only change coordinates, keeping the frame inert. The change of frames is only attainable by boosts in the classical and relativistic regimes for both Galileo and Lorentz (Poincaré) groups. Besides providing a nontrivial example of application of category theory in physics, we also fulfill the presented gap when one directly applies group theory for connecting frames.</span></div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"92 3","pages":"Pages 291-307"},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139061694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Gradient Gibbs measures of an SOS model with alternating magnetism on Cayley trees 具有交替磁性的 SOS 模型在 Cayley 树上的梯度吉布斯度量
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2023-12-01 DOI: 10.1016/S0034-4877(23)00082-4
N.N. Ganikhodjaev , N.M. Khatamov , U.A. Rozikov
{"title":"Gradient Gibbs measures of an SOS model with alternating magnetism on Cayley trees","authors":"N.N. Ganikhodjaev ,&nbsp;N.M. Khatamov ,&nbsp;U.A. Rozikov","doi":"10.1016/S0034-4877(23)00082-4","DOIUrl":"10.1016/S0034-4877(23)00082-4","url":null,"abstract":"<div><div>The work is devoted to gradient Gibbs measures (GGMs) of an SOS model with countable set \u0000\t\t\t\t<span><math><mrow><mi>Z</mi></mrow></math></span><span> of spin values and having alternating magnetism on Cayley trees. This model is defined by a nearest-neighbour gradient interaction potential. Using Külske-Schriever argument, based on boundary law equations, we give several </span><em>q</em>-height-periodic translations invariant GGMs for <em>q</em> = 2, 3, 4.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"92 3","pages":"Pages 309-322"},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139072304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Index 索引
IF 1 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2023-12-01 DOI: 10.1016/S0034-4877(23)00085-X
{"title":"Index","authors":"","doi":"10.1016/S0034-4877(23)00085-X","DOIUrl":"10.1016/S0034-4877(23)00085-X","url":null,"abstract":"","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"92 3","pages":"Pages 401-402"},"PeriodicalIF":1.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139062009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the even-indexed eigenfunctions of the quantum harmonic oscillator 量子谐振子的偶指数本征函数
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2023-10-01 DOI: 10.1016/S0034-4877(23)00069-1
John M. Campbell
{"title":"On the even-indexed eigenfunctions of the quantum harmonic oscillator","authors":"John M. Campbell","doi":"10.1016/S0034-4877(23)00069-1","DOIUrl":"https://doi.org/10.1016/S0034-4877(23)00069-1","url":null,"abstract":"<div><p>In 2021, Fassari et al. introduced a remarkable summation involving the even-indexed eigenfunctions of the quantum harmonic oscillator, and introduced a proof, based on manipulations of multiple elliptic integrals, for an evaluation involving Catalan's constant for the aforementioned summation. This motivates the development of generalizations and extensions of this evaluation. In this article, we show, using the Wilf–Zeilberger method, how this series evaluation may be extended to infinite families of hypergeometric expressions that have free parameters and that are explicitly evaluable in terms of the digamma function. We also consider how an identity related to a nonterminating <em>q</em>-Pfaff–Saalschütz sum due to Krattenthaler and Srivastava may be applied to further generalize the main result due to Fassari et al.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"92 2","pages":"Pages 197-207"},"PeriodicalIF":0.8,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71766814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An unbounded generalization of tomita's observable algebras III 富田可观测代数的无界推广III
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2023-10-01 DOI: 10.1016/S0034-4877(23)00072-1
Hiroshi Inoue
{"title":"An unbounded generalization of tomita's observable algebras III","authors":"Hiroshi Inoue","doi":"10.1016/S0034-4877(23)00072-1","DOIUrl":"https://doi.org/10.1016/S0034-4877(23)00072-1","url":null,"abstract":"<div><p>In this paper we shall continue the studies of <em>T</em><sup>†</sup>-algebras done in [<span>8</span>, <span>9</span>], and above all we investigate decompositions of the vector representation part of a <em>T</em><sup>†</sup>-algebra and apply the results to invariant positive sesquilinear forms on *-algebras.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"92 2","pages":"Pages 243-258"},"PeriodicalIF":0.8,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71766863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Constraints and interactions in quantization of Yukawa model with higher-order derivatives 具有高阶导数的Yukawa模型量化中的约束和相互作用
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2023-10-01 DOI: 10.1016/S0034-4877(23)00067-8
Jan Żochowski
{"title":"Constraints and interactions in quantization of Yukawa model with higher-order derivatives","authors":"Jan Żochowski","doi":"10.1016/S0034-4877(23)00067-8","DOIUrl":"https://doi.org/10.1016/S0034-4877(23)00067-8","url":null,"abstract":"<div><p>This work is dedicated to quantization of the light-front Yukawa model in <em>D</em> = 1 + 3 dimensions with higher-order derivatives of a scalar field. The problem of computing Dirac brackets and the (anti-)commutator algebra of interacting fields in the presence of constraints is discussed. The Dirac method and the Ostrogradski formalism of the higher-order derivatives are exploited. The systematic method of obtaining the inverse of the functional Dirac–Bergmann matrix with interactions and higher-order derivatives is introduced in two variants. The discussion of applications and details of these two variants are conducted. The results of quantization in the form of the (anti-)commutator algebra are presented and analyzed. There is a particular emphasis on the structure of interactions for the light-front Yukawa model with higher-order derivatives.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"92 2","pages":"Pages 145-172"},"PeriodicalIF":0.8,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71766812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A metrical approach to finsler geometry 芬斯勒几何的一种测量方法
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2023-10-01 DOI: 10.1016/S0034-4877(23)00068-X
E. Minguzzi
{"title":"A metrical approach to finsler geometry","authors":"E. Minguzzi","doi":"10.1016/S0034-4877(23)00068-X","DOIUrl":"https://doi.org/10.1016/S0034-4877(23)00068-X","url":null,"abstract":"<div><p>In the standard approach to Finsler geometry the metric is defined as a vertical Hessian and the Chern or Cartan connections appear as just two among many possible natural linear connections on the pullback tangent bundle. Here it is shown that the Hessian nature of the metric, the nonlinear connection and the Chern or Cartan connections can be derived from a few compatibility axioms between metric and Finsler connection. This result provides a metrical formulation of Finsler geometry which is well adapted to field theory, and which has proved useful in Einstein–Cartan-like approaches to Finsler gravity.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"92 2","pages":"Pages 173-195"},"PeriodicalIF":0.8,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71766816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Magnetostatic levitation and two related linear pdes in unbounded domains 无界域内的静磁悬浮和两种相关线性粒子
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2023-10-01 DOI: 10.1016/S0034-4877(23)00066-6
Bartosz Bieganowski, Jakub Siemianowski, Tomasz Cieślak
{"title":"Magnetostatic levitation and two related linear pdes in unbounded domains","authors":"Bartosz Bieganowski,&nbsp;Jakub Siemianowski,&nbsp;Tomasz Cieślak","doi":"10.1016/S0034-4877(23)00066-6","DOIUrl":"https://doi.org/10.1016/S0034-4877(23)00066-6","url":null,"abstract":"<div><p>We consider a problem occurring in a magnetostatic levitation. The problem leads to a linear PDE in a strip. In engineering literature a particular solution is obtained. Such a solution enables one to compute lift and drag forces of the levitating object. It is in agreement with the experiment. We show that such a solution is unique in a class of bounded regular functions. Moreover, as a byproduct, we obtain nonstandard uniqueness results in two linear PDEs in unbounded domains. One of them is an eigenvalue problem for the Laplacian in the strip in the nonstandard class of functions.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"92 2","pages":"Pages 135-144"},"PeriodicalIF":0.8,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71766862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ground state energies of the hubbard models and the hartree–fock approximation hubbard模型和hartree-fock近似的基态能量
IF 0.8 4区 物理与天体物理
Reports on Mathematical Physics Pub Date : 2023-10-01 DOI: 10.1016/S0034-4877(23)00071-X
Jacek Wojtkiewicz, Piotr H. Chankowski
{"title":"Ground state energies of the hubbard models and the hartree–fock approximation","authors":"Jacek Wojtkiewicz,&nbsp;Piotr H. Chankowski","doi":"10.1016/S0034-4877(23)00071-X","DOIUrl":"https://doi.org/10.1016/S0034-4877(23)00071-X","url":null,"abstract":"<div><p>According to the ‘folk knowledge', the Hartree–Fock (H-F) approximation applied to the Hubbard model becomes exact in the limit of small coupling <em>U</em> (the smaller |<em>U|</em>, the better is the H-F approximation). In [<span>1</span>] Bach and Poelchau have substantiated a certain version of this assertion by providing a rigorous estimate of the difference between the true ground-state energy of the simplest version of the Hubbard model and the H-F approximation to this quantity. In this paper we extend their result in two directions: (i) we show how to apply it to the system the hopping matrix of which has period greater than 1 (the case without strict translational invariance) — this allows us to consider systems the dispersion function of which is not (as assumed in [<span>1</span>]) a Morse function; (ii) we point out that the same technique allows to establish analogous estimates for a class of multiband Hubbard models.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"92 2","pages":"Pages 227-241"},"PeriodicalIF":0.8,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71766813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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