Irreversibility and dissipation in finite-state automata

Ganesh, Natesh; Anderson, Neal G.

doi:10.1016/j.physleta.2013.10.010

Cited by 29 publications

(9 citation statements)

References 11 publications

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“…They derive it in a quantum mechanical context, but the same analysis holds for classical systems undergoing Markovian dynamics. As a final comment, instead of viewing the systems considered in [132] as a version of FAs, those systems can be viewed as a variant of information ratchets, with the added restriction that the ratchet is not allowed to change the state of an input symbol after reading it. Accordingly, the reader may want to compare the analysis in [132] with the analyses in Section XIII.…”

Section: A Entropy Dynamics Of Fas In a Steady Statementioning

confidence: 99%

The stochastic thermodynamics of computation

Wolpert¹

2019

J. Phys. A: Math. Theor.

139

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One of the central concerns of computer science is how the resources needed to perform a given computation depend on that computation. Moreover, one of the major resource requirements of computers -ranging from biological cells to human brains to highperformance (engineered) computers -is the energy used to run them, i.e., the thermodynamic costs of running them. Those thermodynamic costs of performing a computation have been a long-standing focus of research in physics, going back (at least) to the early work of Landauer, in which he argued that the thermodynamic cost of erasing a bit in any physical system is at least kT ln [2].One of the most prominent aspects of computers is that they are inherently nonequilibrium systems. However, the research by Landauer and co-workers was done when non-equilibrium statistical physics was still in its infancy, requiring them to rely on equilibrium statistical physics. This limited the breadth of issues this early research could address, leading them to focus on the number of times a bit is erased during a computation -an issue having little bearing on the central concerns of computer science theorists.Since then there have been major breakthroughs in nonequilibrium statistical physics, leading in particular to the new subfield of "stochastic thermodynamics". These breakthroughs have allowed us to put the thermodynamic analysis of bit erasure on a fully formal (nonequilibrium) footing. They are also allowing us to investigate the myriad aspects of the relationship between statistical physics and computation, extending well beyond the issue of how much work is required to erase a bit.In this paper I review some of this recent work on the "stochastic thermodynamics of computation". After reviewing the salient parts of information theory, computer science theory, and stochastic thermodynamics, I summarize what has been learned about the entropic costs of performing a broad range of computations, extending from bit erasure to loop-free circuits to logically reversible circuits to information ratchets to Turing machines. These results reveal new, challenging engineering problems for how to design computers to have minimal thermodynamic costs. They also allow us to start to combine computer science theory and stochastic thermodynamics at a foundational level, thereby expanding both.dergoing arbitrary external driving. In particular, we can now decompose the time-derivative of the (Shannon) entropy of such a system into an "entropy production rate", quantifying the rate of change of the total entropy of the system and its environment, minus a "entropy flow rate", quantifying the rate of entropy exiting the system into its environment. Crucially, the entropy production rate is non-negative, regardless of the CTMC. So if it ever adds a nonzero amount to system entropy, its subsequent evolution cannot undo that increase in entropy. (For this reason it is sometimes referred to as irreversible entropy production.) This is the modern understanding of the second law of thermodynamics, for...

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Section: A Entropy Dynamics Of Fas In a Steady Statementioning

confidence: 99%

The stochastic thermodynamics of computation

Wolpert¹

2019

J. Phys. A: Math. Theor.

139

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“…As argued elsewhere 3,4,5,6 , an appropriate b A loophole that would "save" this measure is the requirement that all reset states of the system have zero entropy, but this is clearly too restrictive. Zero-entropy states are hard to come by in reality, and scenarios are easily identified where information is erased by resetting systems to states with nonzero entropy (e.g.…”

Section: Landauer Erasure Of Referential Informationmentioning

confidence: 99%

Irreversible information loss: Fundamental notions and entropy costs

Anderson

2014

Int. J. Mod. Phys. Conf. Ser.

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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.

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“…In this work, we offer a new analysis, based on our "referential approach" to physical information theory [9][10][11][12], to a Demon that operates a generalized quantum-mechanical Szilard engine in a cycle analogous to Fahn's. The referential approach is based on an overtly relational conception of information, similar in spirit to that adopted by Fahn in his analysis of the Demon, which views physical information exclusively in terms of correlation (i.e., as mutual information) and is well suited for fundamental analyses of dissipation in information processing scenarios.…”

Section: Memory Resetmentioning

confidence: 99%

“…We begin by sketching the "referential" approach to physical information theory [9][10][11][12] that we use to analyze Maxwell's Demon in this work and by introducing key definitions and notation. The referential approach aims to provide a fundamental physical description of classical information processing and its physical costs in globally closed, multicomponent quantum systems.…”

Section: Referential Physical Informationmentioning

confidence: 99%

Conditioning, Correlation and Entropy Generation in Maxwell’s Demon

Anderson

2013

Entropy

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Maxwell's Demon conspires to use information about the state of a confined molecule in a Szilard engine (randomly frozen into a state subspace by his own actions) to derive work from a single-temperature heat bath. It is widely accepted that, if the Demon can achieve this at all, he can do so without violating the Second Law only because of a counterbalancing price that must be paid to erase information when the Demon's memory is reset at the end of his operating cycle. In this paper, Maxwell's Demon is analyzed within a "referential" approach to physical information that defines and quantifies the Demon's information via correlations between the joint physical state of the confined molecule and that of the Demon's memory. On this view, which received early emphasis in Fahn's 1996 classical analysis of Maxwell's Demon, information is erased not during the memory reset step of the Demon's cycle, but rather during the expansion step, when these correlations are destroyed. Dissipation and work extraction are analyzed here for a Demon that operates a generalized quantum mechanical Szilard engine embedded in a globally closed composite, which also includes a work reservoir, a heat bath and the remainder of the Demon's environment. Memory-engine correlations lost during the expansion step, which enable extraction of work from the Demon via operations conditioned on the memory contents, are shown to be dissipative when this decorrelation is achieved unconditionally so no work can be extracted. Fahn's essential conclusions are upheld in generalized form, and his quantitative results supported via appropriate specialization to the Demon of his classical analysis, all without external appeal to classical thermodynamics, the Second Law, phase space conservation arguments or Landauer's Principle.

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Irreversibility and dissipation in finite-state automata

Cited by 29 publications

References 11 publications

The stochastic thermodynamics of computation

The stochastic thermodynamics of computation

Irreversible information loss: Fundamental notions and entropy costs

Conditioning, Correlation and Entropy Generation in Maxwell’s Demon

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