Two Approaches to the Description of the Evolution of Thermodynamic Systems

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3 Citations (Scopus)

Abstract

This paper analyses two approaches to the description of thermodynamic evolution. The first approach describes the dynamics of a thermodynamic system by contact vector fields extended with inputs and outputs while the second One interprets the. thermodynamic vector field as a smooth section of the tangent bundle of the respective Legendre manifold parametrized by n functions, called thermodynamic controls. It is shown that there is a duality between these two approaches similar to the one found in the symplectic case. However, there are still many open questions which present a waste opportunity for further research. 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)34-39
Number of pages6
JournalIFAC-PapersOnLine
Volume49
Issue number24
DOIs
Publication statusPublished - 2016
Event2nd IFAC Workshop on Thermodynamic Foundations for a Mathematical Systems Theory (TFMST) - Vigo
Duration: 28 Sep 201630 Sep 2016

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title = "Two Approaches to the Description of the Evolution of Thermodynamic Systems",
abstract = "This paper analyses two approaches to the description of thermodynamic evolution. The first approach describes the dynamics of a thermodynamic system by contact vector fields extended with inputs and outputs while the second One interprets the. thermodynamic vector field as a smooth section of the tangent bundle of the respective Legendre manifold parametrized by n functions, called thermodynamic controls. It is shown that there is a duality between these two approaches similar to the one found in the symplectic case. However, there are still many open questions which present a waste opportunity for further research. 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.",
keywords = "Mathematical modeling, Thermodynamics, Contact geometry, HAMILTONIAN-SYSTEMS",
author = "Dmitry Gromov",
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N2 - This paper analyses two approaches to the description of thermodynamic evolution. The first approach describes the dynamics of a thermodynamic system by contact vector fields extended with inputs and outputs while the second One interprets the. thermodynamic vector field as a smooth section of the tangent bundle of the respective Legendre manifold parametrized by n functions, called thermodynamic controls. It is shown that there is a duality between these two approaches similar to the one found in the symplectic case. However, there are still many open questions which present a waste opportunity for further research. 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

AB - This paper analyses two approaches to the description of thermodynamic evolution. The first approach describes the dynamics of a thermodynamic system by contact vector fields extended with inputs and outputs while the second One interprets the. thermodynamic vector field as a smooth section of the tangent bundle of the respective Legendre manifold parametrized by n functions, called thermodynamic controls. It is shown that there is a duality between these two approaches similar to the one found in the symplectic case. However, there are still many open questions which present a waste opportunity for further research. 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

KW - Mathematical modeling

KW - Thermodynamics

KW - Contact geometry

KW - HAMILTONIAN-SYSTEMS

U2 - 10.1016/j.ifacol.2016.10.749

DO - 10.1016/j.ifacol.2016.10.749

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JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

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