Microscopic Derivation of an Isothermal Thermodynamic Transformation
Olla, Stefano (2014), Microscopic Derivation of an Isothermal Thermodynamic Transformation, in Cédric Bernardin, Patricia Gonçalves, From Particle Systems to Partial Differential Equations Particle Systems and PDEs, Braga, Portugal, December 2012, Springer : Berlin Heidelberg, p. 225-238. 10.1007/978-3-642-54271-8_10
TypeCommunication / Conférence
External document linkhttps://arxiv.org/abs/1310.0798v1
Book titleFrom Particle Systems to Partial Differential Equations Particle Systems and PDEs, Braga, Portugal, December 2012; Particle Systems and PDEs Conference
Book authorCédric Bernardin, Patricia Gonçalves
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Abstract (EN)We obtain macroscopic isothermal thermodynamic transformations by space-time scalings of a microscopic Hamiltonian dynamics in contact with a heat bath. The microscopic dynamics is given by a chain of anharmonic oscillators subject to a varying tension (external force) and the contact with the heat bath is modeled by independent Langevin dynamics acting on each particle. After a diffusive space-time scaling and cross-graining, the profile of volume converges to the solution of a deterministic diffusive equation with boundary conditions given by the applied tension. This defines an irreversible thermodynamic transformation from an initial equilibrium to a new equilibrium given by the final tension applied. Quasi static reversible isothermal transformations are then obtained by a further time scaling. Heat is defined as the total flux of energy exchanged between the system and the heat bath. Then we prove that the relation between the limit heat, work, free energy and thermodynamic entropy agree with the first and second principle of thermodynamics.
Subjects / Keywordsquasi static transformations; Clausius Inequality; Isothermal transformations; non-equilibrium statistical mechanics; hydrodynamic limit
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