In the framework of classical statistical mechanics, the evolution of a closed system is typically described by the second law of thermodynamics, which states that the entropy of an isolated system tends to increase over time. Entropy is often associated with the level of disorder or randomness in a system.
According to the probabilistic nature of statistical mechanics, it is technically possible, although highly improbable, for a system to spontaneously fluctuate to a state of lower entropy. However, the probability of such a fluctuation occurring in a macroscopic system, especially for systems with a large number of particles, is vanishingly small.
The reason for this is that the number of microstates (configurations consistent with a given macrostate) corresponding to low entropy is significantly smaller than the number of microstates associated with high entropy. As a result, the probability of randomly transitioning from a high entropy state to a low entropy state is astronomically low, making it effectively impossible within observable time scales and system sizes.
It's worth noting that the above discussion applies to closed systems obeying classical statistical mechanics. Quantum systems, on the other hand, can exhibit certain phenomena such as quantum tunneling and quantum fluctuations that allow for non-zero probabilities of transitioning between different states, including states with different levels of entropy. However, even in quantum systems, the probability of such transitions typically decreases exponentially with increasing entropy differences.
In summary, while there is a non-zero, albeit exceedingly small, probability for a closed system to evolve from a high entropy state to a low entropy state, it is highly unlikely to occur in practice due to the overwhelmingly larger number of high entropy microstates compared to low entropy microstates.