Abstract
Using a standard representation of a free energy associated with a linear memory constitutive relation, a new condition, involving linear functionals, is derived which, if satisfied, ensures that the free energy is a functional of the minimal state. Using this condition and results on constructing free energy functionals in Chap. 17, it is shown that if the kernel of the rate of dissipation functional is given by sums of products, the associated free energy functional is a FMS. Because this condition is linear rather than a quadratic, it is easier to explore and to apply in new contexts.
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References
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Amendola, G., Fabrizio, M., Golden, J. (2021). Minimal States and Periodic Histories. In: Thermodynamics of Materials with Memory. Springer, Cham. https://doi.org/10.1007/978-3-030-80534-0_18
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DOI: https://doi.org/10.1007/978-3-030-80534-0_18
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