Time-dependent, irreversible entropy production and geodynamics

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 368, Issue 1910, 2010, Pages 285-300

  Regenauer Lieb, Klaus ^a,b   Karrech, Ali ^b   Chua, Hui Tong ^a   Horowitz, Franklin G ^a   Yuen, Dave ^c  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^b CSIRO   (Australia)

^c UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Carnot efficiency; Endoreversible engine; Finite time thermodynamics; Irreversible entropy; Limit theorems; Plasticity theory

Indexed keywords

CONTINUUM MECHANICS; ELASTICITY; EQUATIONS OF MOTION; GEODYNAMICS; HEAT EXCHANGERS; HEAT TRANSFER; PLASTICITY; STRAIN RATE; STRESSES;

CARNOT EFFICIENCY; ENDOREVERSIBLE; ENDOREVERSIBLE ENGINE; ENTROPY LIMIT; FINITE TIME THERMODYNAMICS; PLASTICITY THEORY;

ENTROPY;

EID: 73849088075     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2009.0204     Document Type: Article

References (27)

1. Alfe, D., Gillan, M. J. & Price, G. D. 2002 Composition and temperature of the Earth's core constrained by combining ab initio calculations and seismic data. Earth Planet. Sci. Lett. 195, 91-98. (doi:10.1016/S0012-821X(01)00568-4)
2. Andresen, B., Salamon, P. & Stephen Berry, R. 1984 Thermodynamics in finite time. Phys. Today 37, 62-70. (doi:10.1063/1.2916405)
3. Ben Zion, Y. 2008 Collective behaviour of earthquakes and faults: continuum discrete transitions, progressive evolutionary changes and different dynamic regimes. Rev. Geophys. 46, 1-70.
4. Bishop, J. F. W. 1953 On the complete solution to problems of deformation of a plastic-rigid material. J. Mech. Phys. Solids 2, 43-53. (doi:10.1016/0022-5096(53)90026-X)
5. Bonetti, E., Colli, P. & Frémond, M. 2005 Entropy balance versus energy balance: application to the heat equation and to phase transitions. In Mechanical modelling and computational issues in civil engineering (eds M. Frémond & F. Maceri), pp. 379-388. Lecture Notes in Applied and Computational Mechanics, vol. 23. Berlin, Germany: Springer-Verlag.
6. Callen, H. 1985 Thermodynamics and an introduction to thermo-statistics. New York, NY: John Wiley and Sons.
7. Castillo, V. & Hoover, W. 1998 Entropy production and Lyapunov instability at the onset of turbulent convection. Phys. Rev. E 58, 7350-7354. (doi:10.1103/PhysRevE.58.7350)
8. Cengel, Y. & Boles, M. 2007 Thermodynamics: an engineering approach. Boston, MA: McGraw Hill.
9. Curzon, F. L. & Ahlborn, B. 1975 Efficiency of a Carnot engine at maximum power output. Am. J. Phys. 43, 22-26. (doi:10.1119/1. 10023)
10. Glansdorff, P., Prigogine, I. & Hill, R. N. 1973 Thermodynamics theory of structure, stability and fluctuations. Am. J. Phys. 41, 147-148. (doi:10.1119/1.1987158)
11. Gordon, J. & Huleihil, M. 1992 General performance characteristics of real heat engines. J. Appl. Phys. 72, 829-837. (doi:10.1063/1.351755)
12. Hill, R. 1951 On the state of stress in a plastic-rigid body at the yield point. Philos. Mag. 42, 868-875.
13. Hirose, K., Brodholt, J., Lay, T. & Yuen, D. 2007 Post Perovskite: the last mantle phase transition. AGU Monograph. New York, NY: AGU Publications. Houlsby, G. & Puzrin, A. 2007 Principles of hyperplasticity, an approach to plasticity theory based on thermodynamic principles. Berlin, Germany: Springer.
14. Knittle, E. & Jeanloz, R. 1991 Earths core-mantle boundary-results of experiments at high- pressures and temperatures. Science 251, 1438-1443. (doi:10.1126/science.251.5000.1438)
15. Lemaitre, J. & Chaboche, J.-L. 1994 Mechanics of solid materials. Cambridge, UK: Cambridge University Press.
16. Moresi, L. & Solomatov, V. 1998 Mantle convection with a brittle lithosphere: thoughts on the global tectonic styles of the Earth and Venus. Geophys. J. Int. 133, 669-682. (doi:10.1046/ j.1365-246X.1998. 00521.x)
17. Onsager, L. 1931 Reciprocal relations in irreversible processes. Phys. Rev. 38, 2265. (doi:10.1103/ PhysRev.38.2265)
18. Ozawa, H., Ohmura, A., Lorenz, R. D. & Pujol, T. 2003 The second law of thermodynamics and the global climate system: a review of the maximum entropy production principle. Rev. Geophys. 41, 1018. (doi:10.1029/2002RG000113)
19. Paltridge, G. W. 1979 Climate and thermodynamic systems of maximum dissipation. Nature 279, 630-631. (doi:10.1038/279630a0)
20. Pons, M. & Le Quere, P. 2005 An example of entropy balance in natural convection. Part 1. The usual Boussinesq equations. C. R. Mecanique 333, 127-132. (doi:10.1016/j.crme.2004.11.011)
21. Regenauer-Lieb, K. & Yuen, D. 2008 Multiscale brittle-ductile coupling and genesis of slow earthquakes. Pure Appl. Geophys. 165, 523-543. (doi:10.1007/s00024-008-0326-8)
22. Regenauer-Lieb, K., Yuen, D. A. & Fusseis, F. 2009 Landslides, ice quakes, earthquakes: a thermodynamic approach to surface instabilities. Pure Appl. Geophys. 166, 1-24. (doi:10.1007/ s00024-009-0520-3)
23. Rice, J. 1971 Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity. J. Mech. Phys. Solids 19, 433-455. (doi:10.1016/0022- 5096(71)90010-X)
24. Salencon, J. 2002 Confining effect on the bearing capacity of circular footings on a purely cohesive soil. C. R. Mecanique 330, 521-525. (doi:10.1016/S1631-0721(02)01495-X)
25. Stacey, F. D. & Davis, P. 2008 Physics of the Earth. 4th edn. Cambridge, UK: Cambridge University Press.
26. Tolman, R. & Fine, P. 1948 On the irreversible production of entropy. Rev. Mod. Phys. 20, 51-77.
27. Ziegler, H. 1983 An introduction to thermomechanics. Amsterdam, The Netherlands: North Holland.