Entropy: ! ≡ #$%& Ω or ∆S = Q/T

1) Quantity maximized in spontaneous processes

Closed system: S always increases: 2nd law, Δ! ≥ 0.

2) State function for system in equilibrium

3) Reversible process: ∆S = 0

4) Heat Flow: Spontaneous flow hot to cold required by 2nd law

5) Total entropy in a system:

! = ∫-. /0. = ∫-

. 1. 23

6) Macroscopic order/disorder: generally small entropy

contribution

Boltzmann Clausius

Laws of Thermodynamics

• First law Δ" = $ +&• Second law Δ' ≥ 0• Third law ' → 0 as + → 0 (or in general ' → ',)

Spin liquid (“spin ice”)

“Magnetic frustration”

Entropy: ! ≡ #$%& Ω or ∆S = Q/T

1) Quantity maximized in spontaneous processes

Closed system: S always increases: 2nd law, Δ! ≥ 0.

2) State function for system in equilibrium

3) Reversible process: ∆S = 0

4) Heat Flow: Spontaneous flow hot to cold required by 2nd law

5) Total entropy in a system:

! = ∫-. /0. = ∫-

. 1. 23

6) Macroscopic order/disorder : generally small entropy

contribution. But atomic-scale mixing entropy can be large.

Boltzmann Clausius

↢ 5& 67&789% (! − !-)

Entropy: ! ≡ #$%& Ω or ∆S = Q/T

1) Quantity maximized in spontaneous processes

Closed system: S always increases: 2nd law, Δ! ≥ 0.

2) State function for system in equilibrium

3) Reversible process: ∆S = 0

4) Heat Flow: Spontaneous flow hot to cold required by 2nd law

5) Total entropy in a system:

! = ∫-. /0. = ∫-

. 1. 23

6) Macroscopic order/disorder : generally small entropy

contribution. But atomic-scale mixing entropy can be large.

Boltzmann Clausius

only if A and B are distinguishable (Gibbs Paradox). Second Law: ΔS not recoverable!

Szilard engine:

Maruyama, Nori, Vedral; Rev. Mod. Phys. 2007, “The physics of Maxwell’s demon and information”

! = #$% ln2 “for free”

Szilard engine:

Maruyama, Nori, Vedral; Rev. Mod. Phys. 2007, “The physics of Maxwell’s demon and information”

! = #$% ln2 “for free”

Maxwell Demon requires at least 1 bit of recorded information.• Szilard: perhaps cognition process always expels k ln 2 entropy.• Connection of thermodynamic entropy to information entropy. (But note, information contribution very small for most systems!)

Temperature define:

§ 2 separate systems, allowed to gradually exchange heat (no work)

Ω = Ω#Ω$ or Ω = Ω#(&#)Ω$(&()(*+ − &#)

§ Maximize Ω; leads to,

read ch. 3 along with section 4.3.

-.#-&#

= -.$-&$

1 2

Temperature define:

§ 2 separate systems, allowed to gradually exchange heat (no work)

Ω = Ω#Ω$ or Ω = Ω#(&#)Ω$(&()(*+ − &#)

§ Maximize Ω; leads to,

§ General result:

-.#-&#

= -.$-&$

/# = /$Equilibrium condition

1/ =

-.-& 1

1 2

Temperature define & First law:

§ General result:

§ Also yields:

1" =

$%$& '

∆% = )*" Always, not just for ideal gases

Or in general no change in external parameters; no work.

Temperature define & First law:

§ General result:

§ Also yields:

§ Also:

1" =

$%$& '

∆% = )*" Always, not just for ideal gases

Or in general no change in external parameters; no work.

+& = "+% − -+. New general version of 1st Law

Temperature define & First law:

§ General result:

§ Also yields:

§ Also:

1" =

$%$& '

∆% = )*" Always, not just for ideal gases

Or in general no change in external parameters; no work.

+& = "+% − -+. New general version of 1st Law

" = $&$% ' - = − $&

$. /Ch. 10

• ΔS ≥ 0 in spontaneous processes.total S includes all interacting subsystems.

• A closed system (or a set of interacting systems) will become more disordered vs. time.

• Heat will flow spontaneously only from a hot to a cold object.

direction is from the system with larger temperature.

• One cannot extract heat from a reservoir and convert the energy entirely to work.

• You will never be younger than you are now!

Statements of Second Law: