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

Springer Nature Singapore Pte Ltd. — 231 p. — (Springer Theses) — ISBN: 978-981-10-6330-5.When random variables are added, their sum tends to obey the Gaussian distribution regarding their large number limit. This fact is the result of the central limit theorem in probability theory. Thus, fluctuation around the average value is always characterized by the Gaussian distribution, which forms the basis of equilibrium statistical mechanics. Even in nonequilibrium situations, the fluctuation theorem, which is the result of the Gaussian fluctuations, plays an important role. Therefore, properties associated with the Gaussian fluctuations, which are important in many cases, are well understood. Nevertheless, non-Gaussian fluctuations are ubiquitous in nature. This is counter-intuitive because we may consider that non-Gaussian fluctuations should be irrelevant because of the central limit theorem. To understand such situations we need to know the origin and properties of the non-Gaussian fluctuations. In this book, Kiyoshi Kanazawa answers these questions through analysis of the physics of non-Gaussian noise.Introduction to Physics of Fluctuation
Review on Stochastic Theory for Fluctuating Thermal Systems
Markovian Stochastic Processes
Kinetic Theory for Dilute Gas
Langevin Equation and Its Microscopic Derivation
Stochastic Calculus for the Single-Trajectory Analysis
Stochastic Energetics for Langevin Dynamics
Statistical Mechanics for Fluctuating Athermal Systems
Microscopic Derivation of Linear Non-Gaussian Langevin Equation
Analytical Solution to Nonlinear Non-Gaussian Langevin Equation
Stochastic Energetics for Non-Gaussian Stochastic Dynamics
Energy Transport Between Athermal Systems
Energy Pumping from Athermal SystemsAppendix. Technical Notes