T lymphocytes (T cells) play an important role in orchestrating an adaptive immune response in complex organisms. Recent experiments have shown that when T cells recognize antigen presenting cells, a complex and large-scale reorganization of intercellular membrane proteins and cell shape occurs. The resulting motif is implicated in information transfer between T cells and antigen presenting cells, and has been labeled the immunological synapse. Numerical solutions of a mathematical model that incorporates binding kinetics, protein mobility, and down regulation, and membrane mechanics has proven successful in describing some of these observations. In this paper, we analyze the equations that describe this model, and this sheds light on the origins of pattern formation in the immunological synapse. In particular, the thermodynamic considerations and dynamic instabilities that lead to pattern formation in and out of equilibrium are elucidated.