The Entropy of a Markov Chain
This article explores the intersection of thermodynamics and information theory by applying the concept of entropy to Markov chains. It seeks to bridge the gap between physical definitions of entropy and abstract mathematical models of life and equilibrium.
Why it matters
Understanding entropy in stochastic systems provides deeper insights into biological modeling and the theoretical limits of complex systems.
10 2 Share Clausius (1865)¹ defines a quantity called entropy. By decomposing physical processes as a chain of engines, he shows that entropy always increases for irreversible processes. For reversible processes like Carnot's ideal engine, the change in entropy is zero. But when an irreversible process occurs, entropy can never decrease unless energy is applied to a system. This is what is known as the second law of thermodynamics.
And whilst entropy itself may not be measurable with a thermometer or ruler, it is still a useful concept since we can calculate derived quantities from it that are directly measurable.
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