Final answer:
Radioactive decay is an example of a three-state ergodic Markov chain that is not reversible because it features one-way transitions from less stable to more stable states, which cannot spontaneously reverse due to energy-dissipating mechanisms. The correct answer is option C.
Step-by-step explanation:
An example of a three-state ergodic Markov chain that is not reversible is radioactive decay. In radioactive decay, the process by which an unstable atomic nucleus loses energy by radiation, the system transitions from a less stable state to a more stable state over time, and these transitions are one-way. This means that once an atom decays to a more stable form, it does not spontaneously revert to its less stable precursor.
The concept of reversibility in physical processes refers to the ability of a system to return to its original state along the exact path it followed to reach its current state. However, macroscopic processes, like radioactive decay, typically feature irreversible behavior due to energy-dissipating mechanisms such as friction or turbulence, which prevent the system's environment from returning to its original state. Thus, even though radioactive decay can be described by a Markov chain (where the future state depends only on the current state and not on the sequence of events that preceded it), it exemplifies a non-reversible Markov process.