Fluctuations, Linear Response and the Fluctuation-Dissipation Relation · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Noise is a measurement

Science · Thermal & Statistical Physics · ages 22-24
Name ______________________   Date ____________
  1. A resistor with no battery hisses. What is that hiss?

    • Quantum tunneling only
    • Thermal equilibrium noise
    • A broken contact
  2. What equals the energy variance in the canonical ensemble?

    • Temperature squared times heat capacity
    • Temperature divided by heat capacity
    • Heat capacity alone
  3. Relative fluctuations shrink as the system grows.

    Circle one:   True   False

  4. Two samples differ only in heat capacity. Which swings more in energy?

    • The one with smaller heat capacity
    • Both swing identically
    • The one with bigger heat capacity
  5. You measured the rest noise across a resistor. What else do you know?

    • Its resistance when driven
    • Its length in meters
    • Its manufacturing date
  6. A driven measurement gives the response. What can you predict without new data?

    • The equilibrium noise
    • The exact microstate
    • The system age
  7. A nanosystem and a bulk sample share a material. Which swings more, relatively?

    • The bulk sample
    • Both swing equally
    • The nanosystem
  8. A student says the hiss needs a battery. What is wrong?

    • Batteries silence all noise
    • Equilibrium agitation needs no drive
    • Resistors never show resistance
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Noise is a measurement W1-mt_Ibsvdyx7uP-s1

  1. Thermal equilibrium noise · Agitation at rest needs no drive.
  2. Temperature squared times heat capacity · One derivative sets both mean and swing.
  3. True · Swings grow slower than means.
  4. The one with bigger heat capacity · Variance tracks heat capacity.
  5. Its resistance when driven · Noise and dissipation are one number.
  6. The equilibrium noise · The relation runs both directions.
  7. The nanosystem · Small N means large relative swings.
  8. Equilibrium agitation needs no drive · Rest noise is thermal, not driven.
Worksheet · LightMySky