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
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Example I
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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
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Observable : O=x
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Il. Particle in a heat bath
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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
Description:
Explore nonequilibrium response theory in this comprehensive lecture from the Bangalore School on Statistical Physics XI. Delve into fluctuations and responses in nonequilibrium systems, examining linear response around equilibrium and the fluctuation-dissipation theorem. Investigate specific examples like random walks and particles in heat baths to understand practical applications. Learn about equilibrium distributions, Einstein relations, and overdamped diffusion. Gain insights into thermodynamic interpretations and entropy generation along trajectories. Conclude with a Q&A session to reinforce understanding of this advanced topic in statistical physics.