Nonequilibrium Response Theory - Lecture 1
International Centre for Theoretical Sciences via YouTube
Overview
Syllabus
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
Taught by
International Centre for Theoretical Sciences