Boltzmann's version of the Second Law states that the entropy of a closed system will tend to increase over time. This means that in a closed system, the disorder or randomness of the system will naturally increase over time.
Boltzmann's version of the Second Law can be mathematically expressed as S = k ln(W), where S is the entropy of a system, k is the Boltzmann constant, and W is the number of microstates (possible arrangements of particles) in the system. This relationship shows that as the number of microstates increases, so does the entropy.
The negative sign in the equation S = k ln(W) indicates that entropy will always increase over time. This is because ln(W) will always be a positive value, and multiplying it by the negative Boltzmann constant results in a negative value for entropy. This shows that the natural tendency of a closed system is to increase in disorder.
The traditional version of the Second Law states that the total entropy of a closed system will not decrease over time. However, Boltzmann's version is more specific and provides a mathematical relationship between entropy and the number of microstates in a system. It also explains the concept of entropy in terms of the disorder and randomness of a system.
Boltzmann's version of the Second Law applies specifically to closed systems, where there is no exchange of matter or energy with the surroundings. It is a fundamental law of thermodynamics and is applicable to a wide range of systems, from microscopic particles to large-scale systems like the universe.