Physics / advanced
Fluctuating systems away from equilibrium
Study stochastic trajectories, diffusion, response, entropy production, and fluctuation relations with careful distinctions between model assumptions and measurements.
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Module 01 advanced
Fluctuating systems away from equilibrium
Study stochastic trajectories, diffusion, response, entropy production, and fluctuation relations with careful distinctions between model assumptions and measurements.
- 01
Langevin forces and white-noise models
Connect coarse-grained random forces to Wiener increments, track noise units, and distinguish the Itô and Stratonovich interpretations of multiplicative noise.
27 min - 02
Ornstein–Uhlenbeck relaxation
Solve a linear noisy relaxation process, distinguish transient variance from stationary correlation, and connect its steady width to a thermal harmonic trap.
26 min - 03
Diffusion and first-passage problems
Derive first-exit probabilities and mean times from backward equations, impose absorbing or reflecting boundaries, and separate hitting times from ordinary diffusion scales.
28 min - 04
Fokker–Planck stationary probability currents
Derive the current associated with an Itô diffusion, distinguish stationary density from zero flux, and handle spatially varying diffusion without losing its derivative term.
28 min - 05
Detailed balance and time reversal
Distinguish edge-by-edge detailed balance from global stationarity, use cycle products to diagnose driving, and relate reversible path statistics to the parity of observed variables.
27 min - 06
Kubo response and fluctuation–dissipation
Relate a weak force response to equilibrium correlations, derive the overdamped harmonic example, and state the thermal and linear-response assumptions needed for the relation.
29 min - 07
Stochastic work, heat, and entropy
Assign work and heat along overdamped trajectories with explicit signs, preserve the stochastic chain rule, and separate system entropy changes from bath entropy production.
29 min - 08
Jarzynski equality in driven models
Recover an equilibrium free-energy difference from exponential work averaging, verify a discrete quench exactly, and distinguish the ensemble theorem from a finite-sample estimator.
28 min - 09
Crooks relation and forward–reverse protocols
Compare correctly paired forward and reverse work distributions, recover free-energy differences from their ratios, and distinguish protocol reversal from simply replaying final data.
29 min - 10
Active matter and broken equilibrium relations
Derive enhanced diffusion from a persistent telegraph model, distinguish active transport from thermal mobility, and separate coarse-grained predictions from unresolved fuel dissipation.
29 min