<p>Entropy of brain states has been hypothesized to correlate with levels of consciousness and cognitive function, forming the basis of theories such as the Entropic Brain Hypothesis (EBH) and the Critical Brain Hypothesis (CBH). However, exact computation of entropy in neural systems is intractable due to their high-dimensional, nonlinear dynamics. In this paper, we introduce a novel ergodic approach for estimating neural entropy by constructing a first-order Markov chain from spike train sequences. Despite the simplification of non-Markovian neural dynamics, this method provides a computationally tractable proxy for system complexity. Entropy estimates across simulated neural network regimes were consistent with theoretical predictions: low entropy in highly synchronized or inhibited states, intermediate entropy under balanced critical conditions, and higher entropy in diverse network activity. These findings demonstrate that approximate entropy measures can capture meaningful distinctions between neural states, providing a bridge between theoretical neuroscience and practical assessment of cognitive states. Limitations due to non-Markovian dynamics and finite sampling are discussed, and future directions for more accurate models are outlined.</p>