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1. Random walk continuous time
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Classroom Contents
Nonequilibrium Response Theory - Lecture 1
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- 1 Nonequilibrium response theory - 1
- 2 Fluctuations and Response In nonequilibrium
- 3 Plan of the course
- 4 What is response?
- 5 Systems in contact with environment energy/particle exchange
- 6 Response theory: unifying formalism
- 7 General question
- 8 Linear response around Equilibrium
- 9 Equilibrium Response Static
- 10 After an initial relaxation phase system reaches new equilibrium assuming normalizable
- 11 Example I
- 12 Example II
- 13 Equilibrium response Dynamic
- 14 Onsager's Regression Hypothesis
- 15 Fluctuation dissipation theorem
- 16 Can be expressed in other forms:
- 17 To apply to specific systems - dynamics needed
- 18 1. Random walk continuous time
- 19 Observable : O=x
- 20 Il. Particle in a heat bath
- 21 Equilibrium distribution Pegx, v xx exp - B Ux +-
- 22 Special case: free particle
- 23 Einstein relation
- 24 Overdamped diffusion
- 25 Derivation of FDT
- 26 Formal solution px, t = ellipx,0 assuming time-independent
- 27 Perturbation Ux - Ux - Eh, Vx L = Lo + Eh,L do dx
- 28 Linear response
- 29 Thermodynamic interpretation
- 30 Entropy generated along a trajectory
- 31 Equilibrium linear response for state observables is entropic, ie, thermodynamic
- 32 Q&A
