skip to main content

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

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
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 20; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
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