Hidden information in Hamiltonian systems with discrete weights.

Abstract

Statistical mechanics is applied to estimate the maximal capacity per weight (${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$) of a network consisting of N binary units and NC binary weights, where C is the average connectivity. For some range of \ensuremath{\eta}, which measures the average correlation between ${\mathit{J}}_{\mathit{i}\mathit{j}}$ and ${\mathit{J}}_{\mathit{j}\mathit{i}}$, the replica-symmetric solution gives the exact ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$, where in the symmetric limit the capacity per bit is greater than 1. However, for symmetric systems with deeper weight depths, the capacity per bit is less than 1, and no perfect information engine exists.