Abstract
The cluster size distributions of power-law form n ( s ) ∝ s − τ with small exponents 0 < τ < 1 are ubiquitous in many naturally occurring growth processes, where one may expect that aggregation driven cluster growth is poised on the edge of cluster break-up. We propose here a statistical thermodynamics description of such a growth process governed by size dependent aggregation and break-up rates of form s α with 0 < α < 2 . By using the maximum entropy method the energy levels and statistical ensemble corresponding the kinetic model are deduced and α is identified as the inverse of thermodynamic temperature, conjugated in the standard way to the total energy E of the system. In addition, the macroscopic free energy F , the entropy S and the heat capacity C are derived. The thermodynamic behavior of the system strongly suggests that at α ≈ 1 there is a phase transition in growth.
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