Violating the second law of thermodynamics in a dynamical system through equivalence closure via mutual information carriers of a 5-tuple measure space

Second Law ◽

Time And Space ◽

Conservative Systems ◽

Recurrence Theorem ◽

Poincare Recurrence ◽

Time and space average of an ergodic systems following the 5-tuple relations (A,~,J,Σ,μ) through the initial increment from a+bθ to a+c+bθ indicates the entropy to be reserved in the deterministic yet dynamical and conservative systems to hold for the set S_p= S_1 ∑_(i=2)^∞_S_i keeping S as the entropy ∃(S_∞=⋯S_3=S_2 )>S_1 obeying the Poincare ́ recurrence theorem throughout the constant attractor A. This in turn states the facts of the equivalence closure as the property of the induced systems to resemblance an entropy conserving scenarios.

Statistical Mechanics: The Basics

Beyond Chance and Credence ◽

10.1093/oso/9780198865094.003.0007 ◽

2021 ◽

pp. 146-174

Author(s):

Wayne C. Myrvold

Keyword(s):

Statistical Mechanics ◽

Second Law ◽

Mechanical Analogue ◽

Statistical Mechanical ◽

Recurrence Theorem ◽

Poincare Recurrence ◽

This chapter introduces the reader to the basics of statistical mechanics. Gibbsian and neo-Boltzmannian approaches are outlined. It includes a statistical-mechanical analogue of the second law of thermodynamics, and a proof of the Poincaré recurrence theorem. It is argued that the differences between Gibbsian and neo-Boltzmannian approaches have been exaggerated.

Poincaré recurrence, second law of thermodynamics and multipliers on the range of the Fourier transform

Journal of Pseudo-Differential Operators and Applications ◽

10.1007/s11868-013-0070-4 ◽

2013 ◽

Vol 4 (3) ◽

pp. 267-277 ◽

Cited By ~ 1

Author(s):

Xiaoxi Duan

Keyword(s):

Fourier Transform ◽

Second Law ◽

Poincare Recurrence ◽

The Fourier Transform ◽

The Poincaré Recurrence Theorem

Graduate Texts in Mathematics - Measure and Category ◽

10.1007/978-1-4615-9964-7_17 ◽

1971 ◽

pp. 65-69

Author(s):

John C. Oxtoby

Keyword(s):

Recurrence Theorem ◽

Poincare Recurrence ◽

On the Homeomorphisms Which Satisfy the Poincare Recurrence Theorem

Proceedings of the American Mathematical Society ◽

10.2307/2041399 ◽

1976 ◽

Vol 58 (1) ◽

pp. 272

Author(s):

Chung-Wu Ho

Keyword(s):

Recurrence Theorem ◽

Poincare Recurrence ◽

Thermodynamic Modeling for Discrete-Time Large-Scale Dynamical Systems

Stability and Control of Large-Scale Dynamical Systems ◽

10.23943/princeton/9780691153469.003.0009 ◽

2011 ◽

Author(s):

Wassim M. Haddad ◽

Sergey G. Nersesov

Keyword(s):

Dynamical System ◽

Dynamical Systems ◽

Thermodynamic Modeling ◽

Discrete Time ◽

Large Scale ◽

Type Inequality ◽

Second Law ◽

Thermodynamic Models ◽

Definition Of

This chapter describes the thermodynamic modeling of discrete-time large-scale dynamical systems. In particular, it develops nonlinear discrete-time compartmental models that are consistent with thermodynamic principles. Since thermodynamic models are concerned with energy flow among subsystems, the chapter constructs a nonlinear compartmental dynamical system model characterized by conservation of energy and the first law of thermodynamics. It then provides a deterministic definition of entropy for a large-scale dynamical system that is consistent with the classical thermodynamic definition of entropy and shows that it satisfies a Clausius-type inequality leading to the law of entropy nonconservation. The chapter also considers nonconservation of entropy and the second law of thermodynamics, nonconservation of ectropy, semistability of discrete-time thermodynamic models, entropy increase and the second law of thermodynamics, and thermodynamic models with linear energy exchange.

Functional mechanics: Evolution of the moments of distribution function and the Poincaré recurrence theorem

P-Adic Numbers Ultrametric Analysis and Applications ◽

10.1134/s2070046611030046 ◽

2011 ◽

Vol 3 (3) ◽

pp. 205-211 ◽

Cited By ~ 4

Author(s):

Andrey I. Mikhaylov

Keyword(s):

Distribution Function ◽

Recurrence Theorem ◽

Poincare Recurrence ◽

Strong Poincaré recurrence theorem in MV-algebras

Mathematica Slovaca ◽

10.2478/s12175-010-0038-2 ◽

2010 ◽

Vol 60 (5) ◽

Cited By ~ 4

Author(s):

Beloslav Riečan

Keyword(s):

Probability Space ◽

Mv Algebra ◽

Measure Preserving Transformation ◽

Recurrence Theorem ◽

Poincare Recurrence ◽

Poincaré Recurrence ◽

Almost All ◽

Poincare Theorem ◽

Mv Algebras

AbstractThe classical Poincaré strong recurrence theorem states that for any probability space (Ω, ℒ, P), any P-measure preserving transformation T, and any A ∈ ℒ, almost all points of A return to A infinitely many times. In the present paper the Poincaré theorem is proved when the σ-algebra ℒ is substituted by an MV-algebra of a special type. Another approach is used in [RIEČAN, B.: Poincaré recurrence theorem in MV-algebras. In: Proc. IFSA-EUSFLAT 2009 (To appear)], where the weak variant of the theorem is proved, of course, for arbitrary MV-algebras. Such generalizations were already done in the literature, e.g. for quantum logic, see [DVUREČENSKIJ, A.: On some properties of transformations of a logic, Math. Slovaca 26 (1976), 131–137.