Question

Explain qualitatively the basis for the Boltzmann distribution. Never mind the details of the math for the moment. Focus on the trade-offs involved with giving energy to a single oscillator vs. giving that energy to a large object.

Short answer

The loss of energy of a system represents that it saturates to a certain state and when the energy level is more the system fluctuates heavily and cools down to one desirable state.

Step-by-step solution

Understanding the Boltzmann distribution

In this problem, Boltzmann distribution is a probability function used in statistical physics to characterize state of a system of particles, with respect to temperature and energy.

Qualitative explanation about Boltzmann distribution

The system can exist in several states; however, the chance of being in certain subset of states is higher than other.

The chance itself is parameterized over certain property values. As a system loses energy, it saturates to a certain state, when the energy is high, it fluctuates heavily and as it cools down it stabilizes to one of desirable states.

The Maxwell-Boltzmann distribution is given below.