The fluctuation-dissipation theorem for a non-periodic driver

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The discussion centers on understanding the fluctuation-dissipation theorem in the context of a monotonic driving force, such as a shearing gel with elastic properties. The key concern is determining the fraction of stored energy that is dissipated under such conditions, as most existing formulations focus on sinusoidal driving forces. The question arises whether it is feasible to measure this dissipation fraction using only monotonic loading. Clarification is sought regarding the nature of the external force applied to the system. The conversation highlights the complexities of applying traditional theories to non-sinusoidal driving scenarios.
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Hi,
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?
 
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Hi,
you mean something like systematically positive external force?
 
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