Origin of the thermodynamic time arrow demonstrated in a realistic statistical system
It is very “probable” that a microstate belonging to the macrostate will escape to the much more vast region of the macrostate . To maintain the appropriate ratio of volumes of the macrostates and for typical statistical systems, the region of should occupy an area times smaller than the region of , i.e., in our figure it should be vastly smaller than a single electron. Thus, coming back from the macrostate to is extremely improbable.
The time evolution (in arbitrary time units) of the probability density functions and determined by the Stosszahlansatz (3).
A collision of two particles belonging to gases A and B.
The symmetry : The initial velocities of particles colliding within a time are uncorrelated.
Visualization of the symmetry : Many particle collisions with definite velocities and but random impact parameters yield the outgoing velocities (and , not marked in the picture) distributed isotropically in space as viewed in the CM frame of the colliding pair.
The time evolution of the temperature for the gases A and B obtained with the simulation, on the basis of Eqs. (32).
Enlarged plots of the time evolution of the temperature of the gas A made for different numbers of collisions in a single simulation step. All plots refer to the same time period realized in different numbers of steps, depending on .
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