Self-organization from structural refrigeration

The self-organization of a classical current is studied, in an exactly solvable model where both the quantum statistics over microhistories of particles, and the macroscopic phenomenology, can be computed in closed form. It is shown that for thermodynamically reversible systems, the Jaynes formulation of statistical mechanics naturally extends to include explicit macroscopic dynamics and heterogeneities in temperature, while preserving the structure of partition functions, effective potentials, and ground states of the equilibrium theory. Self-organization in such reversible systems is constrained by entropy transport through engine and refrigeration cycles, rather than by diffusion in gradients. Limitations in the ability to decompose such systems sensibly into components with additive entropies, and in the extrapolation of entropy functions from equilibrium forms, are discussed with examples.