Open systems are systems in which both matter and energy can pass in and out of freely. Closed systems are systems where energy but not matter can pass through. Finally, isolated systems are systems wherein neither energy nor matter can enter.
Can there exist a fourth system, where only matter but not energy can pass through?
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There will always be transfer of energy in the form of thermal, kinetic, or chemical/gravitational/elastic potential energy (along with a whole slew of other types) whenever any matter enters a system.
Even if one only considers elementary particles (without KE/CPE/EPE/GPE/etc), even then there is still transfer of thermal energy by convection due to the third law of thermodynamics.