Ransomware attacks have rapidly escalated, posing a significant threat to both individuals and organisations by encrypting critical data and demanding substantial ransoms. A novel approach to detecting ransomware is proposed, which combines the sequential learning capabilities of Long Short-Term Memory (LSTM) networks with entropy-based analysis to capture the distinct behavioral patterns that emerge during ransomware encryption. The integration of these two techniques allows for a more adaptive detection system that can identify previously unseen ransomware strains based on their dynamic alterations of file entropy. The model's performance was rigorously evaluated across multiple ransomware families, demonstrating high levels of accuracy, precision, and recall. While some challenges were observed, particularly in cases involving stealthy encryption strategies or minimal entropy fluctuations, the overall system proved highly effective in detecting ransomware attacks before significant damage occurred. The results indicate that LSTM networks, when paired with entropy analysis, offer a promising avenue for enhancing ransomware detection and providing an advanced solution to mitigate evolving cybersecurity threats.