The Free Energy of a General Computation

Abstract

Starting from Landauer's slogan "information is physical," we revise and modify Landauer's principle stating that the erasure of information has a minimal price in the form of a certain quantity of free energy. We establish a direct link between the erasure cost and the work value of a piece of information, and show that the former is essentially the length of the string's best compression by a reversible computation. We generalize the principle by deriving bounds on the free energy to be invested for --- or gained from, for that matter --- a general computation. We then revisit the second law of thermodynamics and compactly rephrase it (assuming the Church/Turing/Deutsch hypothesis that physical reality can be simulated by a universal Turing machine): Time evolutions are logically reversible --- "the future fully remembers the past (but not necessarily vice versa)." We link this view to previous formulations of the second law, and we argue that it has a particular feature that suggests its "logico-informational" nature, namely simulation resilience: If a computation faithfully simulates a physical process violating the law --- then that very computation procedure violates it as well.

arXiv comment8 pages, 3 figures

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Cited by in corpus (6)

• Thermodynamic costs of Turing Machines
• Energy-Consumption Advantage of Quantum Computation
• Generalized Zurek's bound on the cost of an individual classical or quantum computation
• Thermodynamic optimization of quantum algorithms: On-the-go erasure of qubit registers
• Temperature as Joules per Bit
• Small Sample Limit of the Bennett Acceptance Ratio Method and the Variationally Derived Intermediates