Einstein's random walk and thermal diffusion

• DOI: 10.48550/arxiv.1307.4460
• Publication Date: 2013-01-01
• Authors: Yong‐Jung Kim
• Keywords: 0301 basic medicine; 03 medical and health sciences; Mathematics - Analysis of PDEs; FOS: Mathematics; FOS: Physical sciences; Mathematical Physics (math-ph); 74F05, 60J70, 58J65; Mathematical Physics; Analysis of PDEs (math.AP)

Thermal diffusion has been studied for over 150 years. Despite of the long history and increasing importance phenomenon, physics thermal remains poorly understood. In this paper Ludwig's is explained using Einstein's random walk. The only new structure added spatial heterogeneity walk to reflect temperature gradient diffusion. Hence, length speed are location dependent functions in paper. Then, a mathematical understanding such gives foundation as clearly original homogeneous case Einstein.