Nonequilibrium Response Theory - Lecture 1

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.

Nonequilibrium response theory - 1
Fluctuations and Response In nonequilibrium
Plan of the course
What is response?
Systems in contact with environment energy/particle exchange
Response theory: unifying formalism
General question
Linear response around Equilibrium
Equilibrium Response Static
After an initial relaxation phase system reaches new equilibrium assuming normalizable
Example I
Example II
Equilibrium response Dynamic
Onsager's Regression Hypothesis
Fluctuation dissipation theorem
Can be expressed in other forms:
To apply to specific systems - dynamics needed
1. Random walk continuous time
Observable : O=x
Il. Particle in a heat bath
Equilibrium distribution Pegx, v xx exp - B Ux +-
Special case: free particle
Einstein relation
Overdamped diffusion
Derivation of FDT
Formal solution px, t = ellipx,0 assuming time-independent
Perturbation Ux - Ux - Eh, Vx L = Lo + Eh,L do dx
Linear response
Thermodynamic interpretation
Entropy generated along a trajectory
Equilibrium linear response for state observables is entropic, ie, thermodynamic
Q&A