Reversible Computation

Reversible Computation Avraham Guttman Topics in Biological Physics Prof. Elisha Moses, Dr. Roy Bar-Ziv R. Landauer, IBM J. Res. Dev. 3, 183(1961) Bennett, C. H., IBM J. Res. Dev. 17, 525 (1973) R. Landauer, Physica Scripta. Vol. 35, 88-95, 1987Feynman, Lectures on Computation, 1999

T Reversible Computation - Outline • Thermodynamic Reversibility • Physics of Logic Reversibility • mRNA Transcription 0 1 0 1 0 1

Memory Tape 0 1 0 0

Single Bit Operation 0 1 0 1

Carnot Engine http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/carnot.htm

Carnot Cycle Thermodynamically Reversible

AND - Irreversible gate Loss of Information

T Loss of free energy Physically Loss of Information 0 1

von Neumann – Landauer Limit In each irreversible bit operation:

Information Erasure Erasure Irreversible Process Loss of energy Infinite tape: No need for erasure Nonphysical For N erased bits:

X Physical Reversible Copy Copier Model

Bennetts’ Three-Tape Reversible Computation • Algorithm steps while saving • Copying the output • Retracing the algorithm steps R3 R2 R1 R1-1 R2-1 R3-1 Standard 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 History 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 R1 R2 R3 Copy 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

mRNA Transcription from DNA to protein from DNA to protein

mRNA Transcription =G,C,A,U RNA (N bases) +X-S-P-P-P RNA (N+1 bases) +P-Pi (Triphosphate) (Pyrophosphate) from DNA to protein Transistor:

T Reversible Computation - Outline • Thermodynamic Reversibility • Physics of Logic Reversibility • mRNA Transcription 0 1 0 1 Thank You 0 1

Reversible Computation