Actions with the conservation property.

*(English)*Zbl 0576.73008The author proves that if an action for a system has the conservative property at one state, then it has the conservation property at every state and admits an everywhere defined continuous potential. Extensions of these results appropriate for semi-systems are given. The concept of the path-independence property is introduced, and it is shown that this property is tantamount to the conservative property for systems, but it is stronger than the conservative property for semi-systems. The paper is sharpening the results of B. D. Coleman and D. R. Owen in their reference investigations Arch. Ration. Mech. Anal. 54, 1-104 (1974; Zbl 0306.73004 and ibid. 66, 173-181 (1977; Zbl 0412.93001).

This self-contained paper is of great interest for research workers in thermodynamics.

This self-contained paper is of great interest for research workers in thermodynamics.

Reviewer: Gh.Gr.Ciobanu

##### MSC:

74A15 | Thermodynamics in solid mechanics |

##### Keywords:

actions with the conservation property; conservative property at one state; at every state; everywhere defined continuous potential; semi- systems##### References:

[1] | Bernard D. Coleman, David R. Owen: A mathematical foundation for thermodynamics. Arch. Rational Mech. Anal., 54 (1974), 1-104. · Zbl 0306.73004 |

[2] | Bernard D. Coleman, David R. Owen: On the thermodynamics of semi-systems with restrictions on the accessibility of states. Arch. Rational Mech. Anal., 66 (1977), 173-181. · Zbl 0412.93001 |

[3] | Miroslav Šilhavý: On measures, convex cones, and foundations of thermodynamics, I & II. Czech. J. Phys. B 30 (1980), 841-861 and 961-992. |

[4] | Miroslav Šilhavý: On the second law of thermodynamics I & II. Czech. J. Phys. B 32 (1982), 987-1007 and 1011-1033. |

[5] | Miroslav Šilhavý: Foundations of continuum thermodynamics. To appear in: Proceedings of the Workshop on laws and structure of continuum thermodynamics, University of Minnesota, Minneapolis 1983. Springer. |

[6] | Bernard D. Coleman, David R. Owen: On thermodynamics and elastic-plastic materials. Arch. Rational Mech. Anal. 59 (1975), 25-51. · Zbl 0332.73003 |

[7] | Bernard D. Coleman, David R. Owen: On thermodynamics of elastic-plastic materials with temperature-dependent moduli and yield stresses. Arch. Rational Mech. Anal. 70 (1979), 339-354. · Zbl 0441.73007 |

[8] | Clifford Truesdell: Rational Thermodynamics. Second edition. Springer-Verlag. 1984. |

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