Changes

==Application to molecular behavior==

==Application to molecular behavior==

[[Statistical mechanics]] is the application of probability to enormous numbers like this.  It was developed, along with the [[kinetic theory]], by [[James Clerk Maxwell]], Boltzmann, [[Rudolf Clausius]], Clapeyron, and others, during the 19^th century.  The development of the kinetic theory of gases, statistical mechanics, and thermodynamics revolutionized 19^th century physics.  It was recognized that, while we can't analyze the behavior of every molecule, we can analyze the statistical behavior of macroscopic assemblages.  When gas molecules collide, they can transfer energy in a manner that leads to the principle of ''equipartition of energy''.  This, plus the constraints on conservation of the total energy, leads to the ''Maxwell-Boltzmann'' distribution of molecular energies.  From this, one can deduce the properties of volume, pressure, and temperature, leading to Boyle's law and Charles' law, among others.  Temperature was found to be just the average energy per molecule.  (Actually, the average energy per "degree of freedom".)   

[[Statistical mechanics]] is the application of probability to enormous numbers like this.  It was developed, along with the [[kinetic theory]], by [[James Clerk Maxwell]], [[Ludwig Boltzmann]], [[Rudolf Clausius]], [[Benoît Paul Émile Clapeyron]], and others, during the 19^th century.  The development of the kinetic theory of gases, statistical mechanics, and thermodynamics revolutionized 19^th century physics.  It was recognized that, while we can't analyze the behavior of every molecule, we can analyze the statistical behavior of macroscopic assemblages.  When gas molecules collide, they can transfer energy in a manner that leads to the principle of ''equipartition of energy''.  This, plus the constraints on conservation of the total energy, leads to the ''Maxwell-Boltzmann'' distribution of molecular energies.  From this, one can deduce the properties of volume, pressure, and temperature, leading to Boyle's law and Charles' law, among others.  Temperature was found to be just the average energy per molecule.  (Actually, the average energy per "degree of freedom".)   

The fact that heat only flows downhill, and that entropy never decreases, is now just a consequence of the "most probable distribution" principle, or equipartition principle, from mathematical statistics, albeit at a vastly larger scale.

The fact that heat only flows downhill, and that entropy never decreases, is now just a consequence of the "most probable distribution" principle, or equipartition principle, from mathematical statistics, albeit at a vastly larger scale.