Free Energy, Entropy, and Temperature

\(F = E - TS\).

• where
  • \(F\). is the free energy
    • The nature tries to diminish the free energy.
    • Minimizing $F$ involves a trade-off between energy minimization ($E\downarrow$) and entropy maximization ($S\uparrow$).
  • \(E\). is the energy
    • the internal energy or potential
    • the tendency to reach a low-energy, highly-ordered state (e.g., specific data patterns).”
  • \(S\). is the entropy
    • The statistical measure of microstates
    • a state with higher entropy has a higher probability of occurrence due to the larger number of possible configurations.
  • \(T\). is the temperature
    • Acts as a scaling factor that controls the balance
    • high $T$ promotes exploration (Entropy-driven), while low $T$ promotes exploitation (Energy-driven).