Overview

Full Product Details

Author:   Giovanni Gallavotti
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   Softcover reprint of the original 1st ed. 2014
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 23.50cm
Weight:   4.044kg
ISBN:  

9783319383279

ISBN 10:   3319383272
Pages:   248
Publication Date:   17 September 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

Equilibrium.- Many particles systems: kinematics, timing.- Birth of kinetic theory.- Heat theorem and Ergodic hypothesis.- Least action and heat theorem.- Heat Theorem and Ensembles.- Boltzmann’s equation, entropy, Loschmidt’s paradox.- Conclusion.- Stationary Nonequilibrium.- Thermostats and infinite models.- Finite thermostats.- Examples of nonequilibrium problems.- Initial data.- Finite or infinite thermostats? Equivalence?.- SRB distributions.- Chaotic Hypothesis.- Phase space contraction in continuous time.- Phase space contraction in timed observations.- Conclusions.- Discrete phase space.- Recurrence.- Hyperbolicity: stable & unstable manifolds.- Geometric aspects of hyperbolicity. Rectangles.- Symbolic dynamics and chaos.- Examples of hyperbolic symbolic dynamics.- Coarse graining and discrete phase space.- Coarse cells, phase space points and simulations.- The SRB distribution: its physical meaning.- Other stationary distributions.- Phase space cells and entropy.- Counting phase space cells out of equilibrium.- kB logN entropy or Lyapunov function?.- Fluctuations.- SRB potentials.- Chaos and Markov processes.- Symmetries and time reversal.- Pairing rule and Axiom C.- Large deviations.- Time reversal and fluctuation theorem.- Fluctuation patterns.- Onsager reciprocity, Green-Kubo formula, fluctuation theorem.- Local fluctuations: an example.- Local fluctuations: generalities.- Quantum systems, thermostats and non equilibrium.- Quantum adiabatic approximation and alternatives.- Applications.- Equivalent thermostats.- Granular materials and friction.- Neglecting granular friction: the relevant time scales.- Simulations for granular materials.- Fluids.- Developed turbulence.- Intermittency.- Stochastic evolutions.- Very large fluctuations.- Thermometry.- Processes time scale and irreversibility.- Historical comments.- Proof of the second fundamental theorem.- Collision analysis and equipartition.- Dense orbits: an example.- Clausius’ version of recurrence and periodicity.- Clausius’ mechanical proof of the heat theorem.- Priority discussion of Boltzmann (vs. Clausius ).- Priority discussion: Clausius’ reply.- On the ergodic hypothesis (Trilogy: #1).- Canonical ensemble and ergodic hypothesis (Trilogy: #2).- Heat theorem without dynamics (Trilogy: #3).- Irreversibility: Loschmidt and “Boltzmann’s sea”.- Discrete phase space, count of its points and entropy.- Monocyclic and orthodic systems. Ensembles.- Maxwell 1866.- Appendices.- A Appendix: Heat theorem (Clausius version).- B Appendix: Aperiodic Motions as Periodic with Infinite Period!.- C Appendix: The heat theorem without dynamics.- D Appendix: Keplerian motion and heat theorem.- E Appendix: Gauss’ least constraint principle.- F Appendix: Non smoothness of stable/unstable manifolds.- G Appendix: Markovian partitions construction.- H Appendix: Axiom C.- I Appendix: Pairing theory.- J Appendix: Gaussian fluid equations.- K Appendix: Jarzinsky’s formula.- L Appendix: Evans-Searles’ formula.- M Appendix: Forced pendulum with noise.- N Appendix: Solution Eq.(eM.10).- O Appendix: Iteration for Eq.(eM.10).- P Appendix: Bounds for the theorem in Appendix M.- Q Appendix: Hard spheres, BBGKY hierarchy.- R Appendix: Interpretation of BBGKY equations.- S Appendix: BGGKY; an exact solution (?).- T Appendix: Comments on BGGKY and stationarity.- References.- Index.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions