$$Q_{\min} = k_{\mathrm{B}} T \ln 2$$

Equation 2 · Evolutionary Physics

The Arrow of Time and the Engine of Evolution

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Writing a record redundantly is one thing; erasing one is a different, and thermodynamically cheaper to state, act. Rolf Landauer’s 1961 analysis established that any logically irreversible operation — one whose output does not determine a unique input, such as resetting a one-bit memory from either of two states to a single standard state — must, in an isothermal environment at temperature T , dissipate at least a fixed minimum quantity of heat to the surroundings: $Q_{\min} = k_{\mathrm{B}} T \ln 2$. per bit erased [ 3 ] . The bound follows from Liouville’s theorem: the phase-space volume corresponding to distinguishable logical states cannot be compressed into fewer accessible microstates without…

Meanings in this article

• $T$: the temperature.

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