Overview
Given the defintion of {% \Omega %} as the number of different states in the system, the entropy is defined as
{% S = k \; ln \Omega %}
This formula is similar to (but not the same) as
Entropy in Information Theory
The entropy increases with the number of possible states.
Systems in Thermal Contact
The entropy of a system composed of two parts, {% A %} and {% B %} in thermal contact is the sum of the entropies of the individual parts.
{% S_{total} = k \; ln\Omega = k \; ln(\Omega_A \Omega_B) = S_A + S_B %}