Gibbs phase rule for nonequilibrium steady states

Establish whether a Gibbs phase rule exists for stationary nonequilibrium systems and, if so, derive its explicit form and domain of validity for phase coexistence and constraints under steady driving. Characterize the correct set of independent variables and constraints analogous to equilibrium components, phases, and degrees of freedom, and determine its predictive power for heterogeneous nonequilibrium states.

Background

The Gibbs phase rule F = C − P + 2 is fundamental in equilibrium thermodynamics for predicting degrees of freedom in heterogeneous systems. The notes highlight that, under nonequilibrium steady-state driving, there is no established analogue of this rule, raising uncertainty about how phase diagrams and coexistence constraints should be formulated outside equilibrium.

The authors emphasize that classic equilibrium tools (e.g., Landau theory) lack clear counterparts in driven systems, and even basic questions such as how to define universality or nucleation remain unresolved for nonequilibrium steady states.