Contact topology and non-equilibrium thermodynamics

被引：4

作者：

Entov, Michael ^{[1
]}

Polterovich, Leonid ^{[2
]}

机构：

[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

[2] Tel Aviv Univ, Sch Math Sci, IL-6997801 Tel Aviv, Israel

来源：

NONLINEARITY | 2023年 / 36卷 / 06期

基金：

以色列科学基金会;

关键词：

contact manifold; Hamiltonian flow; non-equilibrium thermodynamics; contact thermodynamics; Ising model; Legendrian submanifold; 82Cxx; 53Dxx; 37Jxx; AUBRY-MATHER THEORY; DYNAMICS; MODEL; TIME;

D O I：

10.1088/1361-6544/acd1ce

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We describe a method, based on contact topology, of showing the existence of semi-infinite trajectories of contact Hamiltonian flows which start on one Legendrian submanifold and asymptotically converge to another Legendrian submanifold. We discuss a mathematical model of non-equilibrium thermodynamics where such trajectories play a role of relaxation processes, and illustrate our results in the case of the Glauber dynamics for the mean field Ising model.

引用

页码：3349 / 3375

页数：27

共 33 条

[1]

Aganagic M, 2014, ADV THEOR MATH PHYS, V18, P827

[2]

Anahory Simoes A., 2020, WORKSHOP JOINT STRUC, P247

[3] Contact symmetries and Hamiltonian thermodynamics [J].

Bravetti, A. ;

Lopez-Monsalvo, C. S. ;

Nettel, F. .

ANNALS OF PHYSICS, 2015, 361 :377-400

[4]

Cieliebak K., 2012, Symplectic geometry of affine complex manifolds

[5]

Eliashberg Y, 2000, GEOM FUNCT ANAL, P560

[6]

Entov M., FILTERED RELATIVE SY

[7] Legendrian persistence modules and dynamics [J].

Entov, Michael ;

Polterovich, Leonid .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2022, 24 (02)

[8] Lagrangian tetragons and instabilities in Hamiltonian dynamics [J].

Entov, Michael ;

Polterovich, Leonid .

NONLINEARITY, 2017, 30 (01) :13-34

[9]

FENICHEL N, 1971, INDIANA U MATH J, V21, P193

[10]

Fried S, 2023, STAT INFER STOCH PRO, V26, P413, DOI 10.1007/s11203-022-09283-7

← 1 2 3 4 →