What type of system allows the transfer of matter through its boundaries?

An open system is defined as one that can exchange both energy and matter with its surroundings. In the context of thermodynamics, this means that substances can enter or leave the system, in addition to energy transfer through heat or work. This characteristic makes open systems particularly relevant in various real-world applications, such as biological processes and chemical reactions occurring in open vessels.

In contrast, an isolated system does not exchange either energy or matter with its surroundings, while a closed system allows for energy exchange but restricts matter transfer. A thermally conductive system describes how well a system can transfer heat but does not inherently address the exchange of matter. Thus, the defining feature of an open system is that it facilitates the transfer of both matter and energy, making it the correct answer.