Abstract
Landauer's Principle (LP) associates an entropy increase with the irreversible loss of information from a physical system. Clear statement, unambiguous interpretation, and proper application of LP requires precise, mutually consistent, and sufficiently general definitions for a set of interlocking fundamental notions and quantities (entropy, information, irreversibility, erasure). In this work, we critically assess some common definitions and quantities used or implied in statements of LP, and reconsider their definition within an alternative “referential” approach to physical information theory that embodies an overtly relational conception of physical information. We prove an inequality on the entropic cost of irreversible information loss within this context, as well as “referential analogs” of LP and its more general restatement by Bennett. Advantages of the referential approach for establishing fundamental limits on the physical costs of irreversible information loss in communication and computing systems are discussed throughout.
Highlights
Interrogating Landauer’s PrincipleA typical statement of the “entropic form” of Landauer’s Principle[1] (LP) goes something like this: LP: Erasure of an amount ∆Ier of information from a physical system unavoidably results in an entropy increase of∆S ≥ kB ln(2)∆Ier (1)where kB is Boltzmann’s constant.A well known generalization of LP due to Bennett[2], hereafter referred to as the “Landauer-Bennett Principle” (LBP), addresses a broader class of operations that includes erasure as a special case: This is an Open Access article published by World Scientific Publishing Company
We explore key aspects of information, entropy, and other fundamental notions as they function collectively in LP, LBP, and other propositions that concern irreversible information loss and its dissipative consequences
Irreversible information loss: Fundamental notions and physical costs processes provided in Bennett’s statement, explicitly recognize that initially the “information” is necessarily held in information-bearing degrees of freedom of the system, and explicitly recognize that loss of information from the information-bearing degrees of freedom could generally increase the entropy of the non-informationbearing degrees of freedom and the environment
Summary
A typical statement of the “entropic form” of Landauer’s Principle[1] (LP) goes something like this: LP: Erasure of an amount ∆Ier of information from a physical system unavoidably results in an entropy increase of. LBP: (A)ny logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information bearing degrees of freedom of the information processing apparatus or its environment These and other statements concerning the dissipative costs of information processing can be interpreted unambiguously only if the key notions and quantities are made precise. We introduce an entropic decomposition, enabled by the referential conception of information, that offers an alternative to the “all or nothing” practice of separating the degrees-of-freedom of a system into those that bear information and those that do not We argue that this decomposition enables an objective physical interpretation of the distinction between “known data” and “random data,” upholding such a distinction while de-anthropomorphizing it. Irreversible information loss: Fundamental notions and physical costs considerations underlie the “referential” approach to irreversible information loss and its dissipative consequences that we have developed and applied elsewhere[3,4,5,6]
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