What is the Ludwig Boltzmann entropy formula?

Boltzmann's entropy formula is a fundamental statistical mechanics equation that connects a system's macroscopic entropy to the number of possible microscopic arrangements of its atoms or molecules. Introduced by Austrian physicist Ludwig Boltzmann in 1877, the formula uses the natural logarithm of these microstates multiplied by the Boltzmann constant. It provides a statistical explanation for the second law of thermodynamics by linking microscopic behavior to macroscopic properties like temperature and pressure.

What we know

• Boltzmann's entropy formula relates a system's entropy to the multiplicity, which is the number of real microstates corresponding to a given macrostate. [2]
• The equation includes the Boltzmann constant, a proportionality factor defined as exactly 1.380649 × 10−23 joules per kelvin. [2, 3]
• Austrian physicist Ludwig Boltzmann introduced the statistical entropy perspective and provided this definition of entropy in 1877. [4, 5]
• Max Planck named the constant kB the Boltzmann constant, and the formula is sometimes referred to as the Boltzmann–Planck equation. [2, 5]

Where to go next

• whoWho was Ludwig Boltzmann?
• the bigger pictureWhat is statistical mechanics?
• how it workedHow is the Boltzmann constant defined?
• what followedWhat is the second law of thermodynamics?
• compared withHow did Rudolf Clausius originally define entropy?
• an unexpected connectionHow does a constant of nature help define the SI unit for temperature?The Boltzmann constant is purposely defined with an exact value to formally anchor and define the SI unit kelvin.

Sources

• [1]Boltzmann's entropy formula (Wikidata Q375553) · CC0 1.0
• [2]Boltzmann's entropy formula · CC BY-SA 4.0
• [3]Boltzmann constant · CC BY-SA 4.0
• [4]Entropy (statistical thermodynamics) · CC BY-SA 4.0
• [5]Ludwig Boltzmann · CC BY-SA 4.0