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Increase in entropy gives us the arrow of time. But is there any quantitative relation between these two quantities that relates the entropy change with time interval?

Any literature/text/paper on this subject?

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If you are willing to accept the idea that, even in an irreversible process, entropy in a non-equilibrium state of a system can be defined locally per unit volume and integrated over the volume of the system to give the overall entropy of the system, then the answer to your question is Yes. See Bird, Stewart, and Lightfoot, Transport Phenomena, Chapter 11, problem 11.D.1 Equation of change of entropy, and see Chapter 24, Section 24.1, THE EQUATION OF CHANGE FOR ENTROPY (which includes diffusion and chemical reaction). These references provide the rate of change of entropy with time during an irreversible process.

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