All Topics  
Molecular chaos

 

 
   Email Print
   Bookmark   Link
 

 

Molecular chaos
 
 
  Topics Molecular chaos Topic Home

In kinetic theory
Kinetic theory

Kinetic theory attempts to explain macroscopic properties of gases, such as pressure, temperature, or volume, by considering their molecule composition and motion ....
 in physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, molecular chaos is the assumption that the velocities of colliding particles are uncorrelated, and independent of position. This assumption, also called in the writings of Boltzmann the Stosszahlansatz (collision number hypothesis), makes many calculations tractable.

In particular, the assumption of molecular chaos was a key element, although initially unrecognised, in Boltzmann's H-theorem
H-theorem

In thermodynamics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the increase in the entropy of an ideal gas in an irreversible process, by considering the Boltzmann equation....
 of 1872, which attempted to use kinetic theory to show that the entropy of a gas prepared in a state of less than complete disorder must inevitably increase, as the gas molecules are allowed to collide.

This drew the objection from Loschmidt that it should not be possible to deduce an irreversible process from time-symmetric dynamics and a time-symmetric formalism: something must be wrong (Loschmidt's paradox
Loschmidt's paradox

Loschmidt's paradox, also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics....
).

The resolution (1895) of this paradox is that the velocities of two particles after a collision are no longer truly uncorrelated.






Discussion
Ask a question about 'Molecular chaos'
Start a new discussion about 'Molecular chaos'
Answer questions from other users
Full Discussion Forum



Encyclopedia


In kinetic theory
Kinetic theory

Kinetic theory attempts to explain macroscopic properties of gases, such as pressure, temperature, or volume, by considering their molecule composition and motion ....
 in physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, molecular chaos is the assumption that the velocities of colliding particles are uncorrelated, and independent of position. This assumption, also called in the writings of Boltzmann the Stosszahlansatz (collision number hypothesis), makes many calculations tractable.

In particular, the assumption of molecular chaos was a key element, although initially unrecognised, in Boltzmann's H-theorem
H-theorem

In thermodynamics, the H-theorem, introduced by Ludwig Boltzmann in 1872, describes the increase in the entropy of an ideal gas in an irreversible process, by considering the Boltzmann equation....
 of 1872, which attempted to use kinetic theory to show that the entropy of a gas prepared in a state of less than complete disorder must inevitably increase, as the gas molecules are allowed to collide.

This drew the objection from Loschmidt that it should not be possible to deduce an irreversible process from time-symmetric dynamics and a time-symmetric formalism: something must be wrong (Loschmidt's paradox
Loschmidt's paradox

Loschmidt's paradox, also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics....
).

The resolution (1895) of this paradox is that the velocities of two particles after a collision are no longer truly uncorrelated. By asserting that it was acceptable to ignore these correlations in the population at times after the initial time, Boltzmann had introduced an element of time asymmetry through the formalism of his calculation.