Contact Hamiltonian Dynamics: The Concept and Its Use

Bravetti, Alessandro

doi:10.3390/e19100535

Cited by 128 publications

(103 citation statements)

References 61 publications

(103 reference statements)

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“…Motivated by the theory of relativity, early treatises presenting a geometric approach to thermodynamics appeared already in the 1930s [1]. More recently we have witnessed the use of Riemannian geometry [2][3][4][5][6][7], contact geometry [8][9][10][11], Poisson and symplectic formulations [12], Finsler geometry [3], symmetric spaces [13] and generalised complex geometry [14], among others.…”

Section: Introductionmentioning

confidence: 99%

On the Contact Geometry and the Poisson Geometry of the Ideal Gas

Isidro

Córdoba

2018

Entropy

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Abstract:We elaborate on existing notions of contact geometry and Poisson geometry as applied to the classical ideal gas. Specifically, we observe that it is possible to describe its dynamics using a 3-dimensional contact submanifold of the standard 5-dimensional contact manifold used in the literature. This reflects the fact that the internal energy of the ideal gas depends exclusively on its temperature. We also present a Poisson algebra of thermodynamic operators for a quantum-like description of the classical ideal gas. The central element of this Poisson algebra is proportional to Boltzmann's constant. A Hilbert space of states is identified and a system of wave equations governing the wavefunction is found. Expectation values for the operators representing pressure, volume and temperature are found to satisfy the classical equations of state.

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Section: Introductionmentioning

confidence: 99%

On the Contact Geometry and the Poisson Geometry of the Ideal Gas

Isidro

Córdoba

2018

Entropy

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“…e.g. [3,5] and references therein for more details on contact geometry. In particular, for any natural m and n the pairs of Lax functions…”

Section: Preliminariesmentioning

confidence: 99%

“…Proof. By definition, proving that (5) admits (7) and (8) amounts to proving that both (7) and (8) are compatible by virtue of (5).…”

Section: New Integrable System With Algebraic Lax Pairmentioning

confidence: 99%

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Integrable (3+1)-dimensional system with an algebraic Lax pair

Sergyeyev

2019

Applied Mathematics Letters

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We present a first example of an integrable (3+1)-dimensional dispersionless system with nonisospectral Lax pair involving algebraic, rather than rational, dependence on the spectral parameter, thus showing that the class of integrable (3+1)-dimensional dispersionless systems with nonisospectral Lax pairs is significantly more diverse than it appeared before. The Lax pair in question is of the type recently introduced in [

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“…Some basics and physical applications of contact Hamiltonian systems are summarized in Ref. [35]. Also for some discussions on nonequilibrium processes in terms of contact geometry, see Ref.…”

mentioning

confidence: 99%

Information and contact geometric description of expectation variables exactly derived from master equations

Goto

Hino

2019

Phys. Scr.

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In this paper a class of dynamical systems describing expectation variables exactly derived from continuous-time master equations is introduced and studied from the viewpoint of differential geometry, where such master equations consist of a set of appropriately chosen Markov kernels. To geometrize such dynamical systems for expectation variables, information geometry is used for expressing equilibrium states, and contact geometry is used for nonequilibrium states. Here time-developments of the expectation variables are identified with contact Hamiltonian vector fields on a contact manifold. Also, it is shown that the convergence rate of this dynamical system is exponential. Duality emphasized in information geometry is also addressed throughout.

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Contact Hamiltonian Dynamics: The Concept and Its Use

Cited by 128 publications

References 61 publications

On the Contact Geometry and the Poisson Geometry of the Ideal Gas

On the Contact Geometry and the Poisson Geometry of the Ideal Gas

Integrable (3+1)-dimensional system with an algebraic Lax pair

Information and contact geometric description of expectation variables exactly derived from master equations

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