History dependence of a two-level system

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Abstract
Glasses have history dependence because they are not in equilibrium. A quantitative understanding of the history dependence of glasses cannot be achieved until we have a quantitative theory of the glass state and the equilibrium glass critical point. But we can still rely on some simple glasslike models to gain some qualitative understanding about them. In this paper, we study the history dependence of a two-level-system model by calculating the linear response of its physical properties to small variations in the thermal history. We calculate the linear response of the mean energy to changes in the temperature—the nonequilibrium analogs of the specific heat. We calculate the linear response of the mean thermodynamic entropy exactly, and the linear response of the entropy probability distribution using matched asymptotic expansions.