Abstract
We address a central unresolved issue in electrorheology, the existence of a critical applied electric
field strength necessary for a liquid-to-solid phase transition in electrorheological fluids with sphere
radii & 50µm. In this regime thermal effects are negligible and the behavior of the system cannot be
described using classical methods of statistical mechanics. We instead model the system using generalized
techniques of statistical mechanics which apply to any ergodic Hamiltonian system. The underlying
probability measure is remarkably similar to that of classical statistical mechanics, though the underlying
physics is quite different. Reminiscent of the Ising model, in our model a critical field strength required to
induce a phase transition is characterized by a physically accesible root of a polynomial. The polynomial
roots are poles of a logarithmic potential representation of the system entropy.
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