Brazilian Journal of Probability and Statistics

Microscopic derivation of an adiabatic thermodynamic transformation

Stefano Olla and Marielle Simon

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Abstract

We obtain macroscopic adiabatic thermodynamic transformations by space–time scalings of a microscopic Hamiltonian dynamics subject to random collisions with the environment. The microscopic dynamics is given by a chain of oscillators subject to a varying tension (external force) and to collisions with external independent particles of “infinite mass”. The effect of each collision is to change the sign of the velocity without changing the modulus. This way the energy is conserved by the resulting dynamics. After a diffusive space–time scaling and coarse-graining, the profiles of volume and energy converge to the solution of a deterministic diffusive system of equations 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 adiabatic transformations are then obtained by a further time scaling. Then we prove that the relations between the limit work, internal energy and thermodynamic entropy agree with the first and second principle of thermodynamics.

Article information

Source
Braz. J. Probab. Stat., Volume 29, Number 2 (2015), 540-564.

Dates
First available in Project Euclid: 15 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1429105601

Digital Object Identifier
doi:10.1214/14-BJPS275

Mathematical Reviews number (MathSciNet)
MR3336879

Zentralblatt MATH identifier
1318.82019

Keywords
Thermodynamics adiabatic transformation hydrodynamic limits thermodynamic entropy relative entropy quasi-static transformation

Citation

Olla, Stefano; Simon, Marielle. Microscopic derivation of an adiabatic thermodynamic transformation. Braz. J. Probab. Stat. 29 (2015), no. 2, 540--564. doi:10.1214/14-BJPS275. https://projecteuclid.org/euclid.bjps/1429105601


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References

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