BOLTZMANN TRANSPORT EQUATION

The Boltzmann Equation

The Boltzmann equation, also called the Boltzmann transport equation (BTE), shows how a stream changes as its temperature changes. It also shows how a large amount, like energy, charge, or particle number, changes in a thermodynamic system.

is the Boltzmann equation.

Ludwig Boltzmann

• Friedrich Ludwig Boltzmann was a great philosopher and physicist in the 1800s.
• He came up with the statistical way to explain the second law of thermodynamics and helped make statistical mechanics what it is today.
• One of the most important advances was Boltzmann's kinetic theory of gas.
• One more name for the Boltzmann equation is the Boltzmann transport equation (BTE).
• It is used to look at how a thermodynamic system behaves statistically when it is not in a state of balance.
• Ludwig Boltzmann came up with it in the year 1872.

Applications of the Boltzmann equation

• The Boltzmann equation is used to find the conservation laws for mass, momentum, charge, and energy. These laws are part of fluid dynamics.
• Hamiltonian mechanics: Different mathematical forms were used to change classical mechanics into Hamiltonian mechanics.
• The quantum theory and violation of particle number: The quantum Boltzmann equation is used to find the number of particles that don't stay the same when they collide. This equation is used a lot in the study of physical cosmology.
• General relativity and astronomy: In general relativity and astronomy, the Boltzmann equation is used to explain how galaxies move.