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Are the geometries of the first and second laws of thermodynamics compatible?
1. | Sección de Metodología y Teoría de la Ciencia, Cinvestav, Av. IPN 2508, C.P. 07360, México, D.F., Mexico |
2. | Departamento de Matemáticas, Universidad Autónoma Metropolitana–Iztapalapa, Av. San Rafael Atlixco 186, C.P. 09340 México, D.F., Mexico |
References:
[1] |
D. E. Blair, "Riemannian Geometry of Contact and Symplectic Manifolds,", $2^{nd}$ edition, (2010).
|
[2] |
W. M. Boothby and H. C. Wang, On contact manifolds,, Ann. of Math., 68 (1958), 721.
doi: 10.2307/1970165. |
[3] |
H. B. Callen, "Thermodynamics: An Introduction to the Physical Theories of Equilibrium Thermostatics and Irreversible Thermodynamics,", John Wiley and Sons, (1960). Google Scholar |
[4] |
Y. Hatakeyama, Some notes on differentiable manifolds with almost contact structures,, Tohoku Math. J., 15 (1963), 176.
doi: 10.2748/tmj/1178243844. |
[5] |
R. Hermann, "Geometry, Physics, and Systems,", Pure and Applied Mathematics, (1973).
|
[6] |
S. Kobayashi, Principal fibre bundles with the 1-dimensional toroidal group,, Toku Math. J., 8 (1956), 29.
|
[7] |
A. Morimoto, On normal almost contact structures with a regularity,, Toku Math. J., 16 (1964), 90.
doi: 10.2748/tmj/1178243735. |
[8] |
R. Mrugala, Geometrical formulation of equilibrium phenomenological thermodynamics,, Reports on Mathematical Physics, 14 (1978), 419.
doi: 10.1016/0034-4877(78)90010-1. |
[9] |
R. Mrugala, Submanifolds in the thermodynamic phase space,, Math. Phys., 21 (1985), 197.
|
[10] |
R. Mrugala, J. D. Nulton, J. C. Schön and P. Salamon, Statistical approach to the geometric structure of thermodynamics,, Phys. Rev. A, 41 (1990), 3156.
doi: 10.1103/PhysRevA.41.3156. |
[11] |
J. Nulton and P. Salamon, Geometry of the ideal gas,, Phys. Rev. A, 31 (1985), 2520.
doi: 10.1103/PhysRevA.31.2520. |
[12] |
G. Ruppeiner, Thermodynamics: A riemannian geometric model,, Phys. Rev. A, 20 (1979), 1608.
doi: 10.1103/PhysRevA.20.1608. |
[13] |
P. Salamon, E. Ihrig and R. S. Berry, A group of coordinate transformations which preserve the metric of Weinhold,, J. Math. Phys., 24 (1983), 2515.
doi: 10.1063/1.525629. |
[14] |
H. Shima, "The Geometry of Hessian Structures,", World Scienfific, (2007).
|
[15] |
F. Weinhold, Metric geometry of equilibrium thermodynamics,, J. Chem. Phys., 63 (1975), 2479.
doi: 10.1063/1.431635. |
[16] |
F. Weinhold, Metric geometry of equilibrium thermodynamics. II. Scaling, homogeneity, and generalized Gibbs-Duhem relations,, J. Chem. Phys., 63 (1975), 2484.
doi: 10.1063/1.431635. |
[17] |
F. Weinhold, Metric geometry of equilibrium thermodynamics. III. Elementary formal structure of a vector-algebraic representation of equilibrium thermodynamics,, J. Chem. Phys., 63 (1975), 2488.
doi: 10.1063/1.431636. |
[18] |
F. Weinhold, Metric geometry of equilibrium thermodynamics. IV. Vector-algebraic evaluation of thermodynamic derivatives,, J. Chem. Phys., 63 (1975), 2496.
doi: 10.1063/1.431637. |
show all references
References:
[1] |
D. E. Blair, "Riemannian Geometry of Contact and Symplectic Manifolds,", $2^{nd}$ edition, (2010).
|
[2] |
W. M. Boothby and H. C. Wang, On contact manifolds,, Ann. of Math., 68 (1958), 721.
doi: 10.2307/1970165. |
[3] |
H. B. Callen, "Thermodynamics: An Introduction to the Physical Theories of Equilibrium Thermostatics and Irreversible Thermodynamics,", John Wiley and Sons, (1960). Google Scholar |
[4] |
Y. Hatakeyama, Some notes on differentiable manifolds with almost contact structures,, Tohoku Math. J., 15 (1963), 176.
doi: 10.2748/tmj/1178243844. |
[5] |
R. Hermann, "Geometry, Physics, and Systems,", Pure and Applied Mathematics, (1973).
|
[6] |
S. Kobayashi, Principal fibre bundles with the 1-dimensional toroidal group,, Toku Math. J., 8 (1956), 29.
|
[7] |
A. Morimoto, On normal almost contact structures with a regularity,, Toku Math. J., 16 (1964), 90.
doi: 10.2748/tmj/1178243735. |
[8] |
R. Mrugala, Geometrical formulation of equilibrium phenomenological thermodynamics,, Reports on Mathematical Physics, 14 (1978), 419.
doi: 10.1016/0034-4877(78)90010-1. |
[9] |
R. Mrugala, Submanifolds in the thermodynamic phase space,, Math. Phys., 21 (1985), 197.
|
[10] |
R. Mrugala, J. D. Nulton, J. C. Schön and P. Salamon, Statistical approach to the geometric structure of thermodynamics,, Phys. Rev. A, 41 (1990), 3156.
doi: 10.1103/PhysRevA.41.3156. |
[11] |
J. Nulton and P. Salamon, Geometry of the ideal gas,, Phys. Rev. A, 31 (1985), 2520.
doi: 10.1103/PhysRevA.31.2520. |
[12] |
G. Ruppeiner, Thermodynamics: A riemannian geometric model,, Phys. Rev. A, 20 (1979), 1608.
doi: 10.1103/PhysRevA.20.1608. |
[13] |
P. Salamon, E. Ihrig and R. S. Berry, A group of coordinate transformations which preserve the metric of Weinhold,, J. Math. Phys., 24 (1983), 2515.
doi: 10.1063/1.525629. |
[14] |
H. Shima, "The Geometry of Hessian Structures,", World Scienfific, (2007).
|
[15] |
F. Weinhold, Metric geometry of equilibrium thermodynamics,, J. Chem. Phys., 63 (1975), 2479.
doi: 10.1063/1.431635. |
[16] |
F. Weinhold, Metric geometry of equilibrium thermodynamics. II. Scaling, homogeneity, and generalized Gibbs-Duhem relations,, J. Chem. Phys., 63 (1975), 2484.
doi: 10.1063/1.431635. |
[17] |
F. Weinhold, Metric geometry of equilibrium thermodynamics. III. Elementary formal structure of a vector-algebraic representation of equilibrium thermodynamics,, J. Chem. Phys., 63 (1975), 2488.
doi: 10.1063/1.431636. |
[18] |
F. Weinhold, Metric geometry of equilibrium thermodynamics. IV. Vector-algebraic evaluation of thermodynamic derivatives,, J. Chem. Phys., 63 (1975), 2496.
doi: 10.1063/1.431637. |
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