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Title: Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics

Abstract

We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called “mirror-image” system. The Lagrangian is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the Lagrangian. Entropy increase in the normal system is balanced by the entropy decrease in the mirror-image system, such that there exists an “integral of evolution” which is a constant. The derivation relies on the property of local equilibrium, which states that the local relations between the thermodynamic quantities in non-equilibrium are the same as in equilibrium.

Authors:
 [1]
  1. School of Applied Sciences, RMIT University, GPO Box 2476, Melbourne, Victoria 3001 (Australia)
Publication Date:
OSTI Identifier:
22415860
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 142; Journal Issue: 20; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; BALANCES; ENTROPY; EQUATIONS; EQUILIBRIUM; EVOLUTION; IMAGES; INTEGRALS; LAGRANGIAN FUNCTION; MIRRORS; SYMMETRY; THERMODYNAMICS; VARIATIONAL METHODS

Citation Formats

Glavatskiy, K. S. Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics. United States: N. p., 2015. Web. doi:10.1063/1.4921558.
Glavatskiy, K. S. Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics. United States. doi:10.1063/1.4921558.
Glavatskiy, K. S. Thu . "Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics". United States. doi:10.1063/1.4921558.
@article{osti_22415860,
title = {Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics},
author = {Glavatskiy, K. S.},
abstractNote = {We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called “mirror-image” system. The Lagrangian is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the Lagrangian. Entropy increase in the normal system is balanced by the entropy decrease in the mirror-image system, such that there exists an “integral of evolution” which is a constant. The derivation relies on the property of local equilibrium, which states that the local relations between the thermodynamic quantities in non-equilibrium are the same as in equilibrium.},
doi = {10.1063/1.4921558},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 20,
volume = 142,
place = {United States},
year = {2015},
month = {5}
}