The measurement problem on classical diffusion process: inverse method on stochastic processes

Abstract

In a high number of diffusive systems, measures are processed to calculate material parameters such as diffusion coefficients, or to verify the accuracy of mathematical models. However, the precision of the parameter determination or of the model relevance depends on the location of the measure itself. The aim of this paper is first to analyse, for a mono-dimensional system, the precision of the measure in relation with its location by an inverse problem algorithm and secondly to examine the physical meaning of the results. Statistical mechanic considerations show that, passing over a time–distance criterion, measurement becomes uncertain whatever the initial conditions. The criterion proves that this chaotic mode is related to the production of anti-entropy at a mesoscopique scale that is in violation to quantum theory about measurement.