In 1870, Scottish physicist James Clerk Maxwell (1831–1879) published his authoritative textbook, Theory of Heat (Longmans, Green, and Co., London).

Maxwell provided a comprehensive mathematical exposition of classical thermodynamics, introduced Maxwell’s Thermodynamic Relations, and presented his celebrated “Maxwell’s Demon” thought experiment.

Maxwell’s Demon Thought Experiment

To illustrate the statistical nature of the Second Law of Thermodynamics, Maxwell proposed a thought experiment:

The Scenario

Consider a gas filled container divided into two chambers ($A$ and $B$) by an insulated wall with a tiny frictionless door. A microscopic intelligent being—Maxwell’s Demon—guards the door:

  1. The Demon observes the individual velocities of approaching gas molecules.
  2. When a fast (hot) molecule approaches from $A$, the Demon opens the door to let it pass into $B$.
  3. When a slow (cold) molecule approaches from $B$, the Demon lets it pass into $A$.

The Apparent Paradox

Over time, chamber $B$ becomes hotter and chamber $A$ becomes colder without external mechanical work, apparently violating Clausius’s Second Law ($\Delta S < 0$)!

Resolution: Information Entropy & Szilard / Landauer Limit

In 1929, Leo Szilard and in 1961 Rolf Landauer resolved Maxwell’s Demon:

  • The Demon must acquire and store information about molecule velocities ($\text{information acquisition} = \Delta S_{\text{info}}$).
  • Erasing 1 bit of memory from the Demon’s quantum/classical brain dissipates energy into the environment:

$$\Delta Q_{\text{dissipated}} \ge k_{\text{B}} T \ln 2$$

Including the Demon’s memory erasure entropy ensures that total cosmic entropy always increases ($\Delta S_{\text{total}} \ge 0$), preserving the Second Law.

Key Takeaways

  • Year: 1870
  • Key Figure: James Clerk Maxwell (Scottish Physicist)
  • Core Discovery: Published Theory of Heat and introduced the Maxwell’s Demon thought experiment.
  • Thermodynamic Relations: Formulated Maxwell’s partial derivative relations ($\frac{\partial T}{\partial V}_S = -\frac{\partial P}{\partial S}_V$).
  • Quantum Relevance: Founded quantum information thermodynamics, Szilard engines, and Landauer’s erasure limit ($\Delta Q = k_{\text{B}} T \ln 2$).