Stochastic Dynamics and Irreversibility

✍ Scribed by Tânia Tomé, Mário J. de Oliveira (auth.)

• Publisher: Springer International Publishing
• Year: 2015
• Tongue: English
• Leaves: 402
• Series: Graduate Texts in Physics
• Edition: 1
• Category: Library

✦ Synopsis

This textbook presents an exposition of stochastic dynamics and irreversibility. It comprises the principles of probability theory and the stochastic dynamics in continuous spaces, described by Langevin and Fokker-Planck equations, and in discrete spaces, described by Markov chains and master equations. Special concern is given to the study of irreversibility, both in systems that evolve to equilibrium and in nonequilibrium stationary states. Attention is also given to the study of models displaying phase transitions and critical phenomena both in thermodynamic equilibrium and out of equilibrium.
These models include the linear Glauber model, the Glauber-Ising model, lattice models with absorbing states such as the contact process and those used in population dynamic and spreading of epidemic, probabilistic cellular automata, reaction-diffusion processes, random sequential adsorption and dynamic percolation. A stochastic approach to chemical reaction is also presented.The textbook is intended for students of physics and chemistry and for those interested in stochastic dynamics.
It provides, by means of examples and problems, a comprehensive and detailed explanation of the theory and its applications.

✦ Table of Contents

Front Matter....Pages i-xii
Random Variables....Pages 1-22
Sequence of Independent Variables....Pages 23-42
Langevin Equation....Pages 43-71
Fokker-Planck Equation I....Pages 73-106
Fokker-Planck Equation II....Pages 107-128
Markov Chains....Pages 129-158
Master Equation I....Pages 159-186
Master Equation II....Pages 187-205
Phase Transitions and Criticality....Pages 207-228
Reactive Systems....Pages 229-256
Glauber Model....Pages 257-272
Systems with Inversion Symmetry....Pages 273-294
Systems with Absorbing States....Pages 295-317
Population Dynamics....Pages 319-333
Probabilistic Cellular Automata....Pages 335-350
Reaction-Diffusion Processes....Pages 351-360
Random Sequential Adsorption....Pages 361-368
Percolation....Pages 369-383
Back Matter....Pages 385-394

✦ Subjects

Mathematical Methods in Physics; Math. Applications in Chemistry; Nonlinear Dynamics; Thermodynamics; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences