What Boltzmann's entropy formula states — S = k ln Ω, connecting microscopic states to macroscopic entropy

What is the Bekenstein-Hawking entropy formula, and how does it relate to the black hole's surface area and event horizon?

S = k * A / (4 * l_p^2), relating entropy to a black hole's surface area

What the Boltzmann distribution describes — probability of a state with energy E is proportional to e^(-E/kT)

Boltzmann distribution: Probability of state E ∝ e^(-E/kT)

What the second law of thermodynamics says — entropy of an isolated system never decreases

Entropy in an isolated system always increases or remains constant

What Landauer's principle resolves — erasing one bit of information dissipates at least kT ln 2 of energy

Landauer's principle states energy dissipation during bit erasure is kT ln(2)

What universality means in phase transitions — different systems show identical critical exponents

Universality in phase transitions: identical critical exponents across diverse systems

What Maxwell's demon thought experiment challenges — can information be used to decrease entropy

Maxwell's demon challenges the second law of thermodynamics by potentially decreasing entropy using information