Statistical Entropy from Boltzmann’s Constant

[Sono Fukushima 2D]

Is statistical entropy equal to a regular entropy? Or is it a different type of entropy not calculated from the other equations. For example, could we use delta S with a statistical entropy to calculate the new entropy or is delta S calculating for a different type of entropy?

[Ishita S 2E]

Thermodynamic entropy is extensive, while statistical mechanics gives a non-extensive expression for entropy. Thermodynamic entropy is a macroscopic concept that describes the disorder of a system, while statistical mechanics uses microscopic probabilities to calculate entropy.

[Gia Leon 2A]

Hi! Okay so... yes they are sorta 'equal' to each other because they measure entropy but... at the same time I have to agree with Ishita! Both kinds of entropy describe disorder or randomness, but they come from different angles—macroscopic vs. microscopic. We can technically use statistical entropy to calculate changes in entropy, butttt we usually stick to classical thermodynamics for most practical situations because it's simpler and works well for large-scale systems :)

I think to answer your question... it's best to categorize them as separate things. They are calculated differently and sorta like... are approached in a separate way as well.

Let's look at them:
Classical Thermodynamic Entropy (ΔS): This is what you usually encounter in thermodynamics. We've seen lots of it so far!! It's about the degree of disorder or randomness in a system. Like, when ice melts into water, it becomes more disordered, so its entropy increases. We calculate ΔS using formulas like ΔS = q_rev/T, where q_rev is the reversible heat exchange and T is the temperature.

Statistical Entropy: This comes from a more detailed perspective. It's about the microscopic behaviors of particles in a system, like how they move and interact. It's related to the number of different ways these particles can be arranged while still looking the same on a larger scale!!! However, like.... actually calculating it usually involves complex statistical mechanics :(. Because... well like, theoretically, you could use statistical entropy to calculate changes in entropy ("ΔS"), but then you're gonna be doing calculations based on microscopic particle behaviors... like what Ishita said! However... that's kinda crazy to deal with if you don't have to hahah

So to answer your question; yes.... but you probably wouldn't want to :)