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Boltzmann's Entropy Formula

S = k ln(W), where S is entropy, k is Boltzmann's constant, and W is the number of microstates corresponding to a given macrostate.
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The statement of the theorem

Let H\mathcal{H} be the Hamiltonian operator governing the system's dynamics in a phase space Γ⊂R6N\Gamma \subset \mathbb{R}^{6N}. Consider an isolated system constrained to an energy shell ΩE={x∈Γ∣E−ϵ≤H(x)≤E+ϵ}\Omega_E = \{ \mathbf{x} \in \Gamma \mid E - \epsilon \le H(\mathbf{x}) \le E + \epsilon \}. The number of accessible microstates, WW, is defined by the volume of this shell in phase space, normalized by the fundamental volume ℏ3N\hbar^{3N}. Formally, W≈Vol(ΩE)h3NW \approx \frac{\text{Vol}(\Omega_E)}{h^{3N}}. The entropy SS is then defined via the Boltzmann relation:\n\nS=kBln⁡(W)\mathcal{S} = k_B \ln(W)
Source: Wikipedia