Deterministic Description

Systems:

• Consist of many ($\sim10^{23}$) particles (atoms or molecules)
• We know something about their interactions

Classical Mechanics:

I know forces and initial conditions. I want to predict the evolution. (F=ma)

Quantum Mechanics:

The problem is the same, but stated differently: I want to know the evolution of wave function . ($i\hbar\,\partial\Psi/\partial t= H \Psi$)

Problems with classical and quantum mechanics:

1.

Need to know initial conditions exactly (Bradbury's butterfly)

2.

Classical mechanics can not solve three body problem exactly--even more difficult with more particles!

Is the problem of Statistical Thermodynamics hopeless? NO!