Second law inequality in viscoelastic materials

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Linear irreversible thermodynamics asserts that the instantaneous local spontaneous entropy production must always be non-negative. However for a viscoelastic fluid this is not always the case. Given the fundamental status of the Second Law, this presents a problem. Recently we have derived the Second Law Inequality from first principles via both the Evans-Searles and the Crooks Fluctuation Theorems. This derivation proves that the ensemble average of the time average of the entropy production is non-negative. The distinction between time averages and instantaneous values has not previously been appreciated. This provides the first known macroscopic consequence of the Fluctuation Theorem. We tested the Second Law Inequality using molecular dynamics simulations of oscillatory shear in the linear regime. The Second Law Inequality is valid for time averaged entropy production. We observe that the ensemble average of the instantaneous entropy production is negative for various time intervals.

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