H-theorem

Boltzmann's H-theorem states that the entropy of a closed system can only increase in the course of time, and must approach a limit as time tends to infinity.

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma \geq 0}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} is the entropy source strength, given by (Eq 36 Chap IX Ref. 2)

$\sigma =-k\sum _{i,j}\int C(f_{i},f_{j})\ln f_{i}d{\mathbf {u} }_{i}$

where the function C() represents binary collisions. At equilibrium, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma = 0} .

See also

• Boltzmann equation
• Second law of thermodynamics

References

1. L. Boltzmann "", Wiener Ber. 63 pp. 275- (1872)
2. Sybren R. De Groot and Peter Mazur "Non-Equilibrium Thermodynamics", Dover Publications