V O L . 3 , D O C . 1 0 a B O L T Z M A N N ’ S P R I N C I P L E 9 reached the bottom (thermodynamic equilibrium). If we raise the particle to a con- siderable height z, then, obviously, it will with the greatest probability sink back down to the bottom (irreversible process) in order then to dance up and down, as before, in its proximity. If this sinking back did not occur in the overwhelming majority of cases, a probability function of the assumed quality could not be valid.– Before I go into other applications of Boltzmann’s equation, I would like to draw a general conclusion about it regarding the mean size of the fluctuations that the parameters of a system perform around the values for ideal thermodynamic equilibrium.[10] are parameters defining the state of a system. The null val- ues for the ’s are chosen so that at thermal equilibrium The work that, according to thermodynamics, would have to be performed in order to bring the system from the state of thermodynamic equilibrium into the state very close to thermodynamic equilibrium characterized by the values is . In order that the system’s energy be the same as before, after the state has been established, the amount of heat must be removed from it, which corre- sponds to a reduction in the system’s entropy by . Thus, if the system has assumed the considered state on its own, its entropy is . If this is plugged into the Boltzmann equation, one obtains In this case, therefore, Gauss’s law of error distribution applies to the deviations of the individual parameters from the values for thermodynamic equilibrium. For the mean work that according to thermodynamics would have to be expended to bring the parameter from equilibrium to the temporal mean in a revers- ible process, one obtains the value . [p. 10] λ1…γn λ λ1 λ2… is 0. = = λ1…γn, A Aν aν 2 -----λν 2 1 n = = G A = G T --- - A T --- = S const 1 T -- - aν 2 -----λν 2 1 n –= W const e N RT - aν 2 -----λ 2 ν 1 –------ = Aν λν λν2 Aν RT 2N ------ -=