General Entropy Production Based on Dynamical Analysis

Part of the Springer Theses book series (Springer Theses)


The classical expression for entropy production is a bilinear product of generalized forces and fluxes. The combination of the Cattaneo-Vernotte model with the classical entropy expression gives a non-quadratic form, which needs to be mended to avoid the paradox of negative entropy production. Based on the thermomass theory, it is shown that the entropy production corresponds to the dissipation of the mechanical energy of thermomass flow. Therefore, the generalized forces in the entropy production should be the friction force rather than the driving force. The friction force is proportional to the heat flux. The general entropy production is thus derived as a quadratic form of heat flux, avoiding the paradox of the negative entropy production. The generalized forces and fluxes in other irreversible transport processes are investigated following the similar framework. The friction forces, driving forces and drift velocities are clarified for these transports and the general entropy production for various transport processes are derived.


Friction Force Drift Velocity Entropy Production Generalize Force Momentum Transport 
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  1. 1.
    Jou D, Casas-Vazquez J, Lebon G (1999) Extended irreversible thermodynamics revisited (1988–98). Rep Prog Phys 62(7):1035Google Scholar
  2. 2.
    Lebon G, Jou D, Casas-Vázquez J (2008) Understanding non-equilibrium thermodynamics. Springer, BerlinCrossRefzbMATHGoogle Scholar
  3. 3.
    Jou D, Casas-Vázquez J, Lebon G (2010) Extended irreversible thermodynamics. Springer, BerlinCrossRefzbMATHGoogle Scholar
  4. 4.
    Cimmelli VA (2009) Different thermodynamic theories and different heat conduction laws. J Non-Equilib Thermodyn 34(4):299–333ADSCrossRefzbMATHGoogle Scholar
  5. 5.
    Criado-Sancho M, Llebot JE (1993) Behavior of entropy in hyperbolic heat conduction. Phys Rev E 47:4104–4107ADSCrossRefGoogle Scholar
  6. 6.
    Casas-Vázquez J, Jou D (1994) Nonequilibrium temperature versus local-equilibrium temperature. Phys Rev E 49(2):1040Google Scholar
  7. 7.
    Casas-Vazquez J, Jou D (2003) Temperature in non-equilibrium states: a review of open problems and current proposals. Rep Prog Phys 66(11):1937Google Scholar
  8. 8.
    Cimmelli VA, Sellitto A, Jou D (2009) Nonlocal effects and second sound in a nonequilibrium steady state. Phys Rev B 79(1):014303ADSCrossRefGoogle Scholar
  9. 9.
    Cimmelli VA, Sellitto A, Jou D (2010) Nonequilibrium temperatures, heat waves, and nonlinear heat transport equations. Phys Rev B 81(5):054301ADSCrossRefGoogle Scholar
  10. 10.
    Cimmelli VA, Sellitto A, Jou D (2010) Nonlinear evolution and stability of the heat flow in nanosystems: beyond linear phonon hydrodynamics. Phys Rev B 82(18):184302ADSCrossRefGoogle Scholar
  11. 11.
    Alvarez FX, Jou D (2008) Size and frequency dependence of effective thermal conductivity in nanosystems. J Appl Phys 103(9):094321ADSCrossRefGoogle Scholar
  12. 12.
    Sellitto A, Alvarez FX, Jou D (2010) Second law of thermodynamics and phonon-boundary conditions in nanowires. J Appl Phys 107(6):064302ADSCrossRefGoogle Scholar
  13. 13.
    Jou D, Criado-Sancho M, Casas-Vázquez J (2010) Heat fluctuations and phonon hydrodynamics in nanowires. J Appl Phys 107(8):084302ADSCrossRefGoogle Scholar
  14. 14.
    Jou D, Cimmelli VA, Sellitto A (2012) Nonlocal heat transport with phonons and electrons: application to metallic nanowires. Int J Heat Mass Transf 55(9):2338–2344CrossRefzbMATHGoogle Scholar
  15. 15.
    Sellitto A, Alvarez FX, Jou D (2012) Geometrical dependence of thermal conductivity in elliptical and rectangular nanowires. Int J Heat Mass Transf 55(11):3114–3120CrossRefGoogle Scholar
  16. 16.
    Sellitto A, Cimmelli VA, Jou D (2013) Entropy flux and anomalous axial heat transport at the nanoscale. Phys Rev B 87(5):054302ADSCrossRefGoogle Scholar
  17. 17.
    Mazur P, de Groot SR (1963) Non-equilibrium thermodynamics. North-Holland, AmsterdamzbMATHGoogle Scholar
  18. 18.
    Vignes A (1966) Diffusion in binary solutions. Variation of diffusion coefficient with composition. Ind Eng Chem Fundam 5(2):189–199CrossRefGoogle Scholar
  19. 19.
    Atkins P, Paula J (2006) Physical chemistry, 8th edn. Oxford University Press, New YorkGoogle Scholar
  20. 20.
    Gallavotti G (1996) Chaotic hypothesis: onsager reciprocity and fluctuation-dissipation theorem. J Stat Phys 84(5–6):899–925ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Havemann RH, Engel PF, Baird JR (2003) Nonlinear correction to Ohm’s law derived from Boltzmann’s equation. Appl Phys Lett 24(8):362–364ADSCrossRefGoogle Scholar
  22. 22.
    Bird R B, Armstrong R C, Hassager O (1987) Dynamics of polymeric liquids, 2nd edn. Wiley, New YorkGoogle Scholar
  23. 23.
    Barnes HA, Hutton JF, Walters K (1989) An introduction to rheology. Elsevier, New YorkzbMATHGoogle Scholar
  24. 24.
    Evans DJ(1988) Rheological properties of simple fluids by computer simulation. Phys Rev A, 23(4):1981Google Scholar
  25. 25.
    Erpenbeck JJ (1984) Shear viscosity of the hard-sphere fluid via nonequilibrium molecular dynamics. Phys Rev Lett 52(15):1333ADSCrossRefGoogle Scholar
  26. 26.
    Yong X, Zhang LT (2012) Nanoscale simple-fluid behavior under steady shear. Phys Rev E 85(5):051202ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Kay JM, Nedderman RM (1985) Fluid mechanics and transfer processes. Cambridge University Press, CambridgezbMATHGoogle Scholar

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© 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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