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Dynamical Analysis of Onsager Reciprocal Relations (ORR)

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Part of the Springer Theses book series (Springer Theses)

Abstract

The original derivation of the Onsager reciprocal relations requires that the generalized flux in the expression of energy production should be the time derivative of system state variable. However, it was found that the commonly selected fluxes can hardly meet this requirement. In this chapter, the unambiguous definition of the generalized forces and fluxes in the entropy production is presented from the thermomass viewpoint. The linear regression of fluctuation is actually a balance between the inertia force and the friction force. Therefore, the time derivative of state variables is the inertia force rather than the driving force. The state variables are thereby defined as the average displacement of transported quantities during fluctuation. They have the length unit, which is in agreement with the displacement of heat proposed by Onsager. For the coupled transport processes, the reciprocal relations are manifested to be the symmetry of the coefficient matrix between the friction forces and the drift velocities. They can be macroscopically derived through the principles of Galilean invariance and the third law of Newtonian dynamics.

Keywords

Heat Flux Friction Force Drift Velocity Entropy Production Generalize Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Onsager L (1931) Reciprocal relations in irreversible processes, I. Phys Rev 37(4):405ADSCrossRefzbMATHGoogle Scholar
  2. 2.
    Onsager L (1931) Reciprocal relations in irreversible processes, II. Phys Rev 38(12):2265ADSCrossRefzbMATHGoogle Scholar
  3. 3.
    Gyarmati I, Gyarmati E (1970) Nonequilibrium thermodynamics. Springer, BerlinzbMATHGoogle Scholar
  4. 4.
    Zeng DL (1991) Engineering nonequilibrium thermodynamics. Sci Press, BeijingGoogle Scholar
  5. 5.
    Coleman BD, Truesdell C (1960) On the reciprocal relations of Onsager. J Chem Phys 33(1):28–31Google Scholar
  6. 6.
    Mazur P, de Groot SR (1963) Nonequilibrium thermodynamics. AmsterdamGoogle Scholar
  7. 7.
    Grimvall G (1981) The electron phonon interaction in metals. AmsterdamGoogle Scholar
  8. 8.
    Onsager L, Machlup S (1953) Fluctuations and irreversible processes. Phys Rev 91(6):1505–1512ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Marconi UMB, Puglisi A, Rondoni L et al (2008) Fluctuation–dissipation: response theory in statistical physics. Phys Rep 461(4):111–195ADSCrossRefGoogle Scholar
  10. 10.
    Gabrielli D, Jona. Lasinio G, Landim C (1996) Onsager reciprocity relations without microscopic reversibility. Phys Rev Lett 77(7):1202–1205ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Astumian RD (2008) Reciprocal relations for nonlinear coupled transport. Phys Rev Lett 101(4):046802ADSCrossRefGoogle Scholar
  12. 12.
    Astumian RD (2009) Generalized fluctuation.dissipation and reciprocal relations for Brownian sieves and molecular machines. Phys Rev E 79(2):02111CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Key Laboratory for Thermal Science and Power Engineering of Ministry of EducationDepartment of Engineering Mechanics, Tsinghua UniversityBeijingChina

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