Computational Reversibility and Landauer’s Limit
Reversible computing asks: can we compute without losing information—and therefore without dissipating energy as heat? Landauer’s principle says erasing one bit costs at least of energy. If a computation is logically reversible (no information erased), in theory it can approach zero energy dissipation.
Landauer’s Bound
For an environment at temperature ,
This is tiny at room temperature (~2.8e-21 J/bit) but nonzero. Any irreversible step—like clearing memory—pays this cost on average.
Reversible Primitives
Universal reversible gates like Toffoli and Fredkin let you build logic without erasing bits. Bennett’s “compute, copy, uncompute” trick captures the pattern: run the computation, clone the outputs you need, then run it backward to return ancilla bits to their inputs so nothing gets discarded. Reversible Turing machines formalize this idea as a bijection between states, showing that full computation is possible without information loss—at the cost of extra space and steps.
Why Care?
Energy density keeps rising while we chase cooler, denser hardware; Landauer’s bound sets a floor on irreversible erasures. Fault tolerance and error correction often add erasing steps, so reversible designs try to minimise how often we pay that cost. Quantum computing is a practical reminder: unitary evolution is reversible; measurement (erasure) is where entropy hits.
Practical Friction
Noise, error correction, and garbage bits push entropy back into the system. Cleaning ancillae cheaply requires careful uncomputation; otherwise you lose the gains. Reversible circuits frequently trade time and space for lower dissipation, and adiabatic designs need slower transitions to stay efficient.
Reversible computing is a reminder that information is physical. Whenever we throw bits away, we pay with heat. The challenge is engineering systems that do useful work while erasing as little as possible.