An apparatus and methods for measuring a thermodynamic potential of a limited physical space associated with a change in symmetry, wherein the limited physical space is characterized by a series of symmetry states having a ground symmetry state and at least one higher symmetry state. In one embodiment of the present invention, the method includes the step of transforming the limited physical space from the ground symmetry state to a higher symmetry state to cause the thermodynamic potential of the limited physical space to change from a first value to a second value. In another embodiment, the ground symmetry state is characterized by a U(1) EM Gauge symmetry, the thermodynamic potential T is in the form of a proton magnetoelectrochemical potential, and the at least one higher symmetry state is characterized by an SU(2) symmetry.
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