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8 pages, 275 KiB

Open AccessArticle

Modified Landauer Principle According to Tsallis Entropy

by Luis Herrera

Entropy 2024, 26(11), 931; https://doi.org/10.3390/e26110931 - 31 Oct 2024

Viewed by 574

Abstract

The Landauer principle establishes a lower bound in the amount of energy that should be dissipated in the erasure of one bit of information. The specific value of this dissipated energy is tightly related to the definition of entropy. In this article, we [...] Read more.

The Landauer principle establishes a lower bound in the amount of energy that should be dissipated in the erasure of one bit of information. The specific value of this dissipated energy is tightly related to the definition of entropy. In this article, we present a generalization of the Landauer principle based on the Tsallis entropy. Some consequences resulting from such a generalization are discussed. These consequences include the modification to the mass ascribed to one bit of information, the generalization of the Landauer principle to the case when the system is embedded in a gravitational field, and the number of bits radiated in the emission of gravitational waves. Full article

(This article belongs to the Special Issue The Landauer Principle and Its Implementations in Physics, Chemistry and Biology: Current Status, Critics and Controversies)

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16 pages, 2897 KiB

Open AccessArticle

Elementary Observations: Building Blocks of Physical Information Gain

by J. Gerhard Müller

Entropy 2024, 26(8), 619; https://doi.org/10.3390/e26080619 - 23 Jul 2024

Viewed by 2157

Abstract

In this paper, we are concerned with the process of experimental information gain. Building on previous work, we show that this is a discontinuous process in which the initiating quantum-mechanical matter–instrument interactions are being turned into macroscopically observable events (EOs). In the course [...] Read more.

In this paper, we are concerned with the process of experimental information gain. Building on previous work, we show that this is a discontinuous process in which the initiating quantum-mechanical matter–instrument interactions are being turned into macroscopically observable events (EOs). In the course of time, such EOs evolve into spatio-temporal patterns of EOs, which allow conceivable alternatives of physical explanation to be distinguished. Focusing on the specific case of photon detection, we show that during their lifetimes, EOs proceed through the four phases of initiation, detection, erasure and reset. Once generated, the observational value of EOs can be measured in units of the Planck quantum of physical action

h = 4.136 \times 10^{- 15} e V s

. Once terminated, each unit of entropy of size

k_{B} = 8.617 \times 10^{- 5} e V / K

, which had been created in the instrument during the observational phase, needs to be removed from the instrument to ready it for a new round of photon detection. This withdrawal of entropy takes place at an energetic cost of at least two units of the Landauer minimum energy bound of

E_{L a} = \ln (2) k_{B} T_{D}

for each unit of entropy of size

k_{B}

. Full article

(This article belongs to the Special Issue The Landauer Principle and Its Implementations in Physics, Chemistry and Biology: Current Status, Critics and Controversies)

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10 pages, 253 KiB

Open AccessArticle

Landauer Principle and the Second Law in a Relativistic Communication Scenario

by Yuri J. Alvim and Lucas C. Céleri

Entropy 2024, 26(7), 613; https://doi.org/10.3390/e26070613 - 22 Jul 2024

Viewed by 1354

Abstract

The problem of formulating thermodynamics in a relativistic scenario remains unresolved, although many proposals exist in the literature. The challenge arises due to the intrinsic dynamic structure of spacetime as established by the general theory of relativity. With the discovery of the physical [...] Read more.

The problem of formulating thermodynamics in a relativistic scenario remains unresolved, although many proposals exist in the literature. The challenge arises due to the intrinsic dynamic structure of spacetime as established by the general theory of relativity. With the discovery of the physical nature of information, which underpins Landauer’s principle, we believe that information theory should play a role in understanding this problem. In this work, we contribute to this endeavour by considering a relativistic communication task between two partners, Alice and Bob, in a general Lorentzian spacetime. We then assume that the receiver, Bob, reversibly operates a local heat engine powered by information, and seek to determine the maximum amount of work he can extract from this device. As Bob cannot extract work for free, by applying both Landauer’s principle and the second law of thermodynamics, we establish a bound on the energy Bob must spend to acquire the information in the first place. This bound is a function of the spacetime metric and the properties of the communication channel. Full article

(This article belongs to the Special Issue The Landauer Principle and Its Implementations in Physics, Chemistry and Biology: Current Status, Critics and Controversies)

18 pages, 957 KiB

Open AccessArticle

Landauer Bound in the Context of Minimal Physical Principles: Meaning, Experimental Verification, Controversies and Perspectives

by Edward Bormashenko

Entropy 2024, 26(5), 423; https://doi.org/10.3390/e26050423 - 15 May 2024

Cited by 2 | Viewed by 2028

Abstract

The physical roots, interpretation, controversies, and precise meaning of the Landauer principle are surveyed. The Landauer principle is a physical principle defining the lower theoretical limit of energy consumption necessary for computation. It states that an irreversible change in information stored in a [...] Read more.

The physical roots, interpretation, controversies, and precise meaning of the Landauer principle are surveyed. The Landauer principle is a physical principle defining the lower theoretical limit of energy consumption necessary for computation. It states that an irreversible change in information stored in a computer, such as merging two computational paths, dissipates a minimum amount of heat

k_{B} T l n 2

per a bit of information to its surroundings. The Landauer principle is discussed in the context of fundamental physical limiting principles, such as the Abbe diffraction limit, the Margolus–Levitin limit, and the Bekenstein limit. Synthesis of the Landauer bound with the Abbe, Margolus–Levitin, and Bekenstein limits yields the minimal time of computation, which scales as

τ_{m i n} ~ \frac{h}{k_{B} T}

. Decreasing the temperature of a thermal bath will decrease the energy consumption of a single computation, but in parallel, it will slow the computation. The Landauer principle bridges John Archibald Wheeler’s “it from bit” paradigm and thermodynamics. Experimental verifications of the Landauer principle are surveyed. The interrelation between thermodynamic and logical irreversibility is addressed. Generalization of the Landauer principle to quantum and non-equilibrium systems is addressed. The Landauer principle represents the powerful heuristic principle bridging physics, information theory, and computer engineering. Full article

(This article belongs to the Special Issue The Landauer Principle and Its Implementations in Physics, Chemistry and Biology: Current Status, Critics and Controversies)

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12 pages, 3364 KiB

Open AccessArticle

Events as Elements of Physical Observation: Experimental Evidence

by J. Gerhard Müller

Entropy 2024, 26(3), 255; https://doi.org/10.3390/e26030255 - 13 Mar 2024

Cited by 2 | Viewed by 3046

Abstract

It is argued that all physical knowledge ultimately stems from observation and that the simplest possible observation is that an event has happened at a certain space–time location

\vec{X} = (\vec{x}, t)

. Considering historic experiments, which have been groundbreaking [...] Read more.

It is argued that all physical knowledge ultimately stems from observation and that the simplest possible observation is that an event has happened at a certain space–time location

\vec{X} = (\vec{x}, t)

. Considering historic experiments, which have been groundbreaking in the evolution of our modern ideas of matter on the atomic, nuclear, and elementary particle scales, it is shown that such experiments produce as outputs streams of macroscopically observable events which accumulate in the course of time into spatio-temporal patterns of events whose forms allow decisions to be taken concerning conceivable alternatives of explanation. Working towards elucidating the physical and informational characteristics of those elementary observations, we show that these represent hugely amplified images of the initiating micro-events and that the resulting macro-images have a cognitive value of 1 bit and a physical value of

W_{o b s} = E_{o b s} τ_{o b s} ≫ h

. In this latter equation,

E_{o b s}

stands for the energy spent in turning the initiating micro-events into macroscopically observable events,

τ_{o b s}

for the lifetimes during which the generated events remain macroscopically observable, and

h

for Planck’s constant. The relative value

G_{o b s} = W_{o b s} / h

finally represents a measure of amplification that was gained in the observation process. Full article

(This article belongs to the Special Issue The Landauer Principle and Its Implementations in Physics, Chemistry and Biology: Current Status, Critics and Controversies)

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14 pages, 527 KiB

Open AccessArticle

On the Precise Link between Energy and Information

by Cameron Witkowski, Stephen Brown and Kevin Truong

Entropy 2024, 26(3), 203; https://doi.org/10.3390/e26030203 - 27 Feb 2024

Cited by 2 | Viewed by 2227

Abstract

We present a modified version of the Szilard engine, demonstrating that an explicit measurement procedure is entirely unnecessary for its operation. By considering our modified engine, we are able to provide a new interpretation of Landauer’s original argument for the cost of erasure. [...] Read more.

We present a modified version of the Szilard engine, demonstrating that an explicit measurement procedure is entirely unnecessary for its operation. By considering our modified engine, we are able to provide a new interpretation of Landauer’s original argument for the cost of erasure. From this view, we demonstrate that a reset operation is strictly impossible in a dynamical system with only conservative forces. Then, we prove that approaching a reset yields an unavoidable instability at the reset point. Finally, we present an original proof of Landauer’s principle that is completely independent from the Second Law of thermodynamics. Full article

(This article belongs to the Special Issue The Landauer Principle and Its Implementations in Physics, Chemistry and Biology: Current Status, Critics and Controversies)

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11 pages, 319 KiB

Open AccessArticle

Thermodynamical versus Logical Irreversibility: A Concrete Objection to Landauer’s Principle

by Didier Lairez

Entropy 2023, 25(8), 1155; https://doi.org/10.3390/e25081155 - 1 Aug 2023

Cited by 3 | Viewed by 1713

Abstract

Landauer’s principle states that the logical irreversibility of an operation, such as erasing one bit, whatever its physical implementation, necessarily implies its thermodynamical irreversibility. In this paper, a very simple counterexample of physical implementation (that uses a two-to-one relation between logic and thermodynamic [...] Read more.

Landauer’s principle states that the logical irreversibility of an operation, such as erasing one bit, whatever its physical implementation, necessarily implies its thermodynamical irreversibility. In this paper, a very simple counterexample of physical implementation (that uses a two-to-one relation between logic and thermodynamic states) is given that allows one bit to be erased in a thermodynamical quasistatic manner (i.e., one that may tend to be reversible if slowed down enough). Full article

(This article belongs to the Special Issue The Landauer Principle and Its Implementations in Physics, Chemistry and Biology: Current Status, Critics and Controversies)

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Figure 1
Expansion of a unit amount of gas from volume V (state A) to <math display="inline"><semantics><mrow><mn>2</mn><mi>V</mi></mrow></semantics></math> (state B) at the same temperature T (in joules). (1) Monothermal expansion with a piston (top): the gas produces work W and pumps heat Q. (2) Adiabatic free expansion (middle): no heat and no work are exchanged with the surroundings. In both cases the cycle is closed using the same restoring process (bottom). In the first case, the net energy cost <math display="inline"><semantics><mrow><msub><mi>E</mi><mrow><mi>cost</mi></mrow></msub><mo>=</mo><mo>−</mo><mi>Q</mi></mrow></semantics></math> of a cycle can be as small as desired (quasistatic, Equation (<a href="#FD3-entropy-25-01155" class="html-disp-formula">3</a>)). In the second case, it has a lower limit of <math display="inline"><semantics><mrow><mi>T</mi><mo form="prefix">ln</mo><mn>2</mn></mrow></semantics></math> (Equation (<a href="#FD4-entropy-25-01155" class="html-disp-formula">4</a>)). Full article ">Figure 2
Landauer’s functional procedure to physically implement the RESET TO 0 (ERASE) logical operation by the means of a thermodynamical bistable potential with a tunable barrier and a bias. Here, the bit is initially set to 1 but the same procedure would apply if the was were set to 0. Full article ">Figure 3
Two-to-one implementation of a bit: quasistatic isothermal compression/expansion of a gas is performed with a transmission of gear ratio 2 (crank–pulley/crankshaft–pulley). The two stable positions of the crank (to which are assigned bit values 0 and 1) correspond to a single stable position of the piston. Full article ">Figure 4
The gear ratio r can be small enough so that thermal fluctuations of the gas below the piston permit the crank-angle (<math display="inline"><semantics><mi>ϕ</mi></semantics></math>) to be in any position. This soft potential well determines a third state (S for “standard”) for a virgin bit. Full article ">

12 pages, 914 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Dissipation during the Gating Cycle of the Bacterial Mechanosensitive Ion Channel Approaches the Landauer Limit

by Uğur Çetiner, Oren Raz, Madolyn Britt and Sergei Sukharev

Entropy 2023, 25(5), 779; https://doi.org/10.3390/e25050779 - 10 May 2023

Cited by 1 | Viewed by 1970

Abstract

The Landauer principle sets a thermodynamic bound of

k_{B} T

ln 2 on the energetic cost of erasing each bit of information. It holds for any memory device, regardless of its physical implementation. It was recently shown that carefully built artificial devices [...] Read more.

The Landauer principle sets a thermodynamic bound of

k_{B} T

ln 2 on the energetic cost of erasing each bit of information. It holds for any memory device, regardless of its physical implementation. It was recently shown that carefully built artificial devices can attain this bound. In contrast, biological computation-like processes, e.g., DNA replication, transcription and translation use an order of magnitude more than their Landauer minimum. Here, we show that reaching the Landauer bound is nevertheless possible with biological devices. This is achieved using a mechanosensitive channel of small conductance (MscS) from E. coli as a memory bit. MscS is a fast-acting osmolyte release valve adjusting turgor pressure inside the cell. Our patch-clamp experiments and data analysis demonstrate that under a slow switching regime, the heat dissipation in the course of tension-driven gating transitions in MscS closely approaches its Landauer limit. We discuss the biological implications of this physical trait. Full article

(This article belongs to the Special Issue The Landauer Principle and Its Implementations in Physics, Chemistry and Biology: Current Status, Critics and Controversies)

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Review

Jump to: Research

12 pages, 298 KiB

Open AccessFeature PaperReview

Landauer Bound and Continuous Phase Transitions

by Maria Cristina Diamantini

Entropy 2023, 25(7), 984; https://doi.org/10.3390/e25070984 - 28 Jun 2023

Viewed by 1614

Abstract

In this review, we establish a relation between information erasure and continuous phase transitions. The order parameter, which characterizes these transitions, measures the order of the systems. It varies between 0, when the system is completely disordered, and 1, when the system is [...] Read more.

In this review, we establish a relation between information erasure and continuous phase transitions. The order parameter, which characterizes these transitions, measures the order of the systems. It varies between 0, when the system is completely disordered, and 1, when the system is completely ordered. This ordering process can be seen as information erasure by resetting a certain number of bits to a standard value. The thermodynamic entropy in the partially ordered phase is given by the information-theoretic expression for the generalized Landauer bound in terms of error probability. We will demonstrate this for the Hopfield neural network model of associative memory, where the Landauer bound sets a lower limit for the work associated with ‘remembering’ rather than ‘forgetting’. Using the relation between the Landauer bound and continuous phase transition, we will be able to extend the bound to analog computing systems. In the case of the erasure of an analog variable, the entropy production per degree of freedom is given by the logarithm of the configurational volume measured in units of its minimal quantum. Full article

(This article belongs to the Special Issue The Landauer Principle and Its Implementations in Physics, Chemistry and Biology: Current Status, Critics and Controversies)

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