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How can one derive a general expression for the entropy production in a system undergoing a non-equilibrium process, such as a non-equilibrium phase transition or a stochastic fluctuation?

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Assume any convenient reversible path connecting the initial and final equilibrium states and apply

$$\Delta S=\int_1^2 \frac {dQ_{rev}}{T}$$

to the path.

For an excellent description of the how and why you can do this, I recommend the following:

https://www.physicsforums.com/insights/grandpa-chets-entropy-recipe/

Hope this helps.

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