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PubMed1984

Collective properties of neural networks: a statistical physics approach.

Among the various models proposed so far to account for the properties of neural networks, the one devised by Little and the one derived by Hopfield prove to be the most interesting because they allow the use of statistical mechanics techniques. The link between the Hopfield model and the statistical mechanics is provided by the existence of an extensive quantity. When the synaptic plasticity behaves according to a Hebbian procedure, the analogy with the classical spin glass models studied by Van Hemmen is complete. In particular exact solutions describing the steady states of noisy systems are found. On the other hand, the Little model introduces a Markovian dynamics. One shows that the evolution equation obeys the microreversibility principle if the synaptic efficiencies are symmetrical. Therefore, assuming that such a symmetry materializes, the Little model has to obey a Gibbs statistics. The corresponding Hamiltonian is derived accordingly. At last, using these results, both models are shown to display associative memory properties. In particular the storage capacity of neural networks working along with the Little dynamics is similar to the capacity of Hopfield neural networks. The conclusion drawn from the study of the Hopfield model can be extended to the Little model, which is certainly a more realistic description of the biological situation.

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PubMed2006

Surface freezing in normal alkanes: a statistical physics approach.

The present paper aims to understand the surface freezing occurring on the interface between liquid normal alkane and air. After proposing a simple microscopic model, it reveals that the model can describe the surface freezing of normal alkanes. Subsequently, surface freezing is immediately proved to be a first order phase transition, which has been illustrated by numerous experiments. Moreover, our calculation predicts a new first order phase transition on the interface. These two transitions correspond to the liquid to monolayer and monolayer to perfect solid transitions, respectively. A phase diagram is obtained directly from the calculations as well. The model indicates that both van der Waals interaction and the entropy influenced by the surface are essential for explaining the surface phase transition.

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