Statistical Mechanics for Athermal Fluctuation: Non-Gaussian Noise in Physics

Description

The author investigates athermal fluctuation from the viewpoints of statistical mechanics in this thesis. Stochastic methods are theoretically very powerful in describing fluctuation of thermodynamic quantities in small systems on the level of a single trajectory and have been recently developed on the basis of stochastic thermodynamics. This thesis proposes, for the first time, a systematic framework to describe athermal fluctuation, developing stochastic thermodynamics for non-Gaussian processes, while thermal fluctuations are mainly addressed from the viewpoint of Gaussian stochastic processes in most of the conventional studies. First, the book provides an elementary introduction to the stochastic processes and stochastic thermodynamics. The author derives a Langevin-like equation with non-Gaussian noise as a minimal stochastic model for athermal systems, and its analytical solution by developing systematic expansions is shown as the main result. Furthermore, the a uthor shows a thermodynamic framework for such non-Gaussian fluctuations, and studies some thermodynamics phenomena, i.e. heat conduction and energy pumping, which shows distinct characteristics from conventional thermodynamics. The theory introduced in the book would be a systematic foundation to describe dynamics of athermal fluctuation quantitatively and to analyze their thermodynamic properties on the basis of stochastic methods. Front Matter ....Pages i-xvi Introduction to Physics of Fluctuation (Kiyoshi Kanazawa)....Pages 1-8 Front Matter ....Pages 9-9 Markovian Stochastic Processes (Kiyoshi Kanazawa)....Pages 11-26 Kinetic Theory for Dilute Gas (Kiyoshi Kanazawa)....Pages 27-39 Langevin Equation and Its Microscopic Derivation (Kiyoshi Kanazawa)....Pages 41-54 Stochastic Calculus for the Single-Trajectory Analysis (Kiyoshi Kanazawa)....Pages 55-71 Stochastic Energetics for Langevin Dynamics (Kiyoshi Kanazawa)....Pages 73-85 Front Matter ....Pages 87-87 Microscopic Derivation of Linear Non-Gaussian Langevin Equation (Kiyoshi Kanazawa)....Pages 89-102 Analytical Solution to Nonlinear Non-Gaussian Langevin Equation (Kiyoshi Kanazawa)....Pages 103-132 Stochastic Energetics for Non-Gaussian Stochastic Dynamics (Kiyoshi Kanazawa)....Pages 133-154 Energy Transport Between Athermal Systems (Kiyoshi Kanazawa)....Pages 155-170 Energy Pumping from Athermal Systems (Kiyoshi Kanazawa)....Pages 171-183 Conclusion (Kiyoshi Kanazawa)....Pages 185-188 Back Matter ....Pages 189-222