Free energy of a general computation

Area of Science:

• Thermodynamics
• Information Theory
• Computer Science
• Physics

Background:

• Landauer's principle posits a physical cost for information erasure.
• The relationship between information, computation, and thermodynamics is a key area of research.
• The second law of thermodynamics governs the direction of natural processes.

Purpose of the Study:

• To revise and modify Landauer's principle concerning the free energy cost of information erasure.
• To establish a direct link between erasure cost and the work value of information.
• To rephrase the second law of thermodynamics in a logico-informational framework.

Main Methods:

• Theoretical analysis and modification of Landauer's principle.
• Derivation of bounds on free energy for general computations.
• Rephrasing the second law of thermodynamics based on the Church-Turing-Deutsch hypothesis.

Main Results:

• The cost of information erasure is directly related to the compressibility of information via reversible computation.
• General bounds for free energy investment or gain in computations were derived.
• A new formulation of the second law emphasizes logical reversibility and simulation resilience.

Conclusions:

• Information erasure cost is fundamentally linked to data compression and reversible computation.
• The second law of thermodynamics can be understood as a principle of logical reversibility in physical systems.
• The logico-informational nature of the second law is highlighted by its simulation resilience property.