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I have been trying to understand the fluctuation-dissipation theorem of statistical physics. I understand the objective: to predict the dissipated and stored power in a system driven to oscillate about thermodynamic equilibrium.

Most formulations I have come across assume a sinusoidal driving force.

My question is this: If we have a monotonic driving force, e.g, a shearing 'gel' (that has some elasticity, i.e, there are both storage and dissipation components), how do we decide what fraction of the stored energy is being dissipated? Is it even possible to measure this fraction through only monotonic loading?