Landscape and flux theory of non-equilibrium dynamical systems with application to biology

Computational properties of use of biological organisms or to the construction of computers can emerge as collective properties of systems having a large number of simple equivalent components (or neurons). The physical meaning of content-addressable memory is described by an appropriate phase space flow of the state of a system. A model of such a system is given, based on aspects of neurobiology but readily adapted to integrated circuits. The collective properties of this model produce a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size. The algorithm for the time evolution of the state of the system is based on asynchronous parallel processing. Additional emergent collective properties include some capacity for generalization, familiarity recognition, categorization, error correction, and time sequence retention. The collective properties are only weakly sensitive to details of the modeling or the failure of individual devices.

An expression is derived for the classical free energy difference between two configurations of a system, in terms of an ensemble of finite-time measurements of the work performed in parametrically switching from one configuration to the other. Two well-known equilibrium identities emerge as limiting cases of this result.

Neurons are often considered to be the computational engines of the brain, with synapses acting solely as conveyers of information. But the diverse types of synaptic plasticity and the range of timescales over which they operate suggest that synapses have a more active role in information processing. Long-term changes in the transmission properties of synapses provide a physiological substrate for learning and memory, whereas short-term changes support a variety of computations. By expressing several forms of synaptic plasticity, a single neuron can convey an array of different signals to the neural circuit in which it operates.