Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics

Journal Article · Thu May 28 04:00:00 EDT 2015 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4921558· OSTI ID:22415860

Glavatskiy, K. S. ^[1]

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1. School of Applied Sciences, RMIT University, GPO Box 2476, Melbourne, Victoria 3001 (Australia)

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.

• OSTI ID: 22415860
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 20 Vol. 142; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BALANCES
ENTROPY
EQUATIONS
EQUILIBRIUM
EVOLUTION
IMAGES
INTEGRALS
LAGRANGIAN FUNCTION
MIRRORS
SYMMETRY
THERMODYNAMICS
VARIATIONAL METHODS