Conversational agents (CAs) are revolutionizing human-computer interaction by evolving from text-based chatbots to empathetic digital humans (DHs) capable of rich emotional expressions. This paper explores the integration of neural and physiological signals into the perception module of CAs to enhance empathetic interactions. By leveraging these cues, the study aims to detect emotions in real-time and generate empathetic responses and expressions. We conducted a user study where participants engaged in conversations with a DH about emotional topics. The DH responded and displayed expressions by mirroring detected emotions in real-time using neural and physiological cues. The results indicate that participants experienced stronger emotions and greater engagement during interactions with the Empathetic DH, demonstrating the effectiveness of incorporating neural and physiological signals for real-time emotion recognition. However, several challenges were identified, including recognition accuracy, emotional transition speeds, individual personality effects, and limitations in voice tone modulation. Addressing these challenges is crucial for further refining Empathetic DHs and fostering meaningful connections between humans and artificial entities. Overall, this research advances human-agent interaction and highlights the potential of real-time neural and physiological emotion recognition in creating empathetic DHs.