Abstract
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.
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References
Jou D, Casas-Vazquez J, Lebon G (1999) Extended irreversible thermodynamics revisited (1988–98). Rep Prog Phys 62(7):1035
Lebon G, Jou D, Casas-Vázquez J (2008) Understanding non-equilibrium thermodynamics. Springer, Berlin
Jou D, Casas-Vázquez J, Lebon G (2010) Extended irreversible thermodynamics. Springer, Berlin
Cimmelli VA (2009) Different thermodynamic theories and different heat conduction laws. J Non-Equilib Thermodyn 34(4):299–333
Criado-Sancho M, Llebot JE (1993) Behavior of entropy in hyperbolic heat conduction. Phys Rev E 47:4104–4107
Casas-Vázquez J, Jou D (1994) Nonequilibrium temperature versus local-equilibrium temperature. Phys Rev E 49(2):1040
Casas-Vazquez J, Jou D (2003) Temperature in non-equilibrium states: a review of open problems and current proposals. Rep Prog Phys 66(11):1937
Cimmelli VA, Sellitto A, Jou D (2009) Nonlocal effects and second sound in a nonequilibrium steady state. Phys Rev B 79(1):014303
Cimmelli VA, Sellitto A, Jou D (2010) Nonequilibrium temperatures, heat waves, and nonlinear heat transport equations. Phys Rev B 81(5):054301
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):184302
Alvarez FX, Jou D (2008) Size and frequency dependence of effective thermal conductivity in nanosystems. J Appl Phys 103(9):094321
Sellitto A, Alvarez FX, Jou D (2010) Second law of thermodynamics and phonon-boundary conditions in nanowires. J Appl Phys 107(6):064302
Jou D, Criado-Sancho M, Casas-Vázquez J (2010) Heat fluctuations and phonon hydrodynamics in nanowires. J Appl Phys 107(8):084302
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):2338–2344
Sellitto A, Alvarez FX, Jou D (2012) Geometrical dependence of thermal conductivity in elliptical and rectangular nanowires. Int J Heat Mass Transf 55(11):3114–3120
Sellitto A, Cimmelli VA, Jou D (2013) Entropy flux and anomalous axial heat transport at the nanoscale. Phys Rev B 87(5):054302
Mazur P, de Groot SR (1963) Non-equilibrium thermodynamics. North-Holland, Amsterdam
Vignes A (1966) Diffusion in binary solutions. Variation of diffusion coefficient with composition. Ind Eng Chem Fundam 5(2):189–199
Atkins P, Paula J (2006) Physical chemistry, 8th edn. Oxford University Press, New York
Gallavotti G (1996) Chaotic hypothesis: onsager reciprocity and fluctuation-dissipation theorem. J Stat Phys 84(5–6):899–925
Havemann RH, Engel PF, Baird JR (2003) Nonlinear correction to Ohm’s law derived from Boltzmann’s equation. Appl Phys Lett 24(8):362–364
Bird R B, Armstrong R C, Hassager O (1987) Dynamics of polymeric liquids, 2nd edn. Wiley, New York
Barnes HA, Hutton JF, Walters K (1989) An introduction to rheology. Elsevier, New York
Evans DJ(1988) Rheological properties of simple fluids by computer simulation. Phys Rev A, 23(4):1981
Erpenbeck JJ (1984) Shear viscosity of the hard-sphere fluid via nonequilibrium molecular dynamics. Phys Rev Lett 52(15):1333
Yong X, Zhang LT (2012) Nanoscale simple-fluid behavior under steady shear. Phys Rev E 85(5):051202
Kay JM, Nedderman RM (1985) Fluid mechanics and transfer processes. Cambridge University Press, Cambridge
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Dong, Y. (2016). General Entropy Production Based on Dynamical Analysis. In: Dynamical Analysis of Non-Fourier Heat Conduction and Its Application in Nanosystems. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48485-2_3
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DOI: https://doi.org/10.1007/978-3-662-48485-2_3
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