It\^o--distribution from Gibbs measure and a comparison with experiment
It\^o--distribution from Gibbs measure and a comparison with experiment
Abstract Langevin dynamics of a confined Brownian particle with coordinate--dependent diffusion involves multiplicative noise. Mathematically, equilibrium of such a stochastic system with multiplicative noise is an It\^o--process. However, in physics literature, the process and resulting It\^o--distribution is not considered to represent equilibrium because it is a modified Boltzmann distribution. It\^o--distribution …