How is the concept of entropy related to the number of microstates available to a system?

The relationship between entropy and the number of microstates in a system is a fundamental concept in statistical thermodynamics. Entropy can be understood as a measure of disorder or randomness, and it quantifies the number of ways a system can be arranged at the microscopic level while still maintaining the same macroscopic parameters (such as energy, volume, and number of particles).

More specifically, the Boltzmann entropy formula gives the relationship:

[ S = k \ln(W) ]

where ( S ) is the entropy, ( k ) is the Boltzmann constant, and ( W ) is the number of microstates available to the system. According to this equation, as the number of microstates ( W ) increases, the entropy ( S ) also increases logarithmically.

This means that when a system can be arranged in a greater number of ways, it exhibits higher entropy. This concept is essential in understanding why systems tend towards states of higher entropy—because those states represent greater configurations and are statistically more likely to occur. Therefore, the correct conclusion is that more microstates correspond to higher entropy, reflecting the inherent diversity of arrangements available to the particles in the system.