The dual klepsydra model of internal time representation and time reproduction.

We present a model of the internal representation and reproduction of temporal durations, the 'dual klepsydra' model (DKM). Unlike most contemporary models operating on a 'pacemaker-counter' scheme, the DKM does not assume an oscillatory process as the internal time-base. It is based on irreversible, dissipative processes in inflow/outflow systems (leaky klepsydrae), whose states are continuously compared; if their states are equal, durations are subjectively perceived as equal. Model-based predictions fit experimental time reproduction data with good accuracy, and show qualitative features not accounted for by other models. The deterministic model is characterized by two parameters, kappa (outflow rate coefficient) and eta (ratio of inflow rates). A stochastic version of the model (SDKM) assumes randomly fluctuating inflows, involves two more parameters, and accounts for intra-individual variance of reproduced durations. Analysis of the SDKM leads to non-trivial problems in the stochastic theory, briefly sketched here. Methods of parameter estimation for both deterministic and stochastic versions are given. Applying the DKM to the subjective experience of time passage, we show how subjective measure of elapsed time is constituted. Finally, essential features of the model and its possible neurophysiological interpretation are discussed.