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Fadler P, Friedenberger A, Lutz E. Efficiency at Maximum Power of a Carnot Quantum Information Engine. PHYSICAL REVIEW LETTERS 2023; 130:240401. [PMID: 37390443 DOI: 10.1103/physrevlett.130.240401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2022] [Accepted: 05/17/2023] [Indexed: 07/02/2023]
Abstract
Optimizing the performance of thermal machines is an essential task of thermodynamics. We here consider the optimization of information engines that convert information about the state of a system into work. We concretely introduce a generalized finite-time Carnot cycle for a quantum information engine and optimize its power output in the regime of low dissipation. We derive a general formula for its efficiency at maximum power valid for arbitrary working media. We further investigate the optimal performance of a qubit information engine subjected to weak energy measurements.
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Affiliation(s)
- Paul Fadler
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
| | - Alexander Friedenberger
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
| | - Eric Lutz
- Institute for Theoretical Physics I, University of Stuttgart, D-70550 Stuttgart, Germany
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2
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Raux P, Ritort F. N-States Continuous Maxwell Demon. ENTROPY (BASEL, SWITZERLAND) 2023; 25:321. [PMID: 36832687 PMCID: PMC9955812 DOI: 10.3390/e25020321] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/31/2022] [Revised: 02/06/2023] [Accepted: 02/07/2023] [Indexed: 06/18/2023]
Abstract
Maxwell's demon is a famous thought experiment and a paradigm of the thermodynamics of information. It is related to Szilard's engine, a two-state information-to-work conversion device in which the demon performs single measurements and extracts work depending on the state measurement outcome. A variant of these models, the continuous Maxwell demon (CMD), was recently introduced by Ribezzi-Crivellari and Ritort where work was extracted after multiple repeated measurements every time that τ is in a two-state system. The CMD was able to extract unbounded amounts of work at the cost of an unbounded amount of information storage. In this work, we built a generalization of the CMD to the N-state case. We obtained generalized analytical expressions for the average work extracted and the information content. We show that the second law inequality for information-to-work conversion is fulfilled. We illustrate the results for N-states with uniform transition rates and for the N = 3 case.
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Affiliation(s)
- Paul Raux
- Université Paris Cité, CNRS, UMR 8236-LIED, 75013 Paris, France
- Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
| | - Felix Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, University of Barcelona, 08028 Barcelona, Spain
- Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028 Barcelona, Spain
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3
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He L, Cheong JW, Pradana A, Chew LY. Effects of correlation in an information ratchet with finite tape. Phys Rev E 2023; 107:024130. [PMID: 36932557 DOI: 10.1103/physreve.107.024130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2022] [Accepted: 01/13/2023] [Indexed: 06/18/2023]
Abstract
With the finite-tape autonomous information ratchet modeled by He et al. [Phys. Rev. E 105, 054131 (2022)2470-004510.1103/PhysRevE.105.054131], we recast the information processing second law, giving a tighter bound on the work extracted, in terms of the marginal bit-ratchet distribution defined from the joint tape-ratchet distribution. The marginal distribution is further utilized to probe and elucidate the conditions that lead to the presence of equilibrium and nonequilibrium stationary states in general, which are related to the effects of correlation. Applying our analysis to two designs of this information ratchet, where correlations within manifest differently, we uncover the mathematical condition for equilibrium stationary states for information ratchets that harness correlation, to identify them for engine operation during the transient phase.
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Affiliation(s)
- Lianjie He
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371
| | - Jian Wei Cheong
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371
| | - Andri Pradana
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371
| | - Lock Yue Chew
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371
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4
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Bhattacharyya D, Jarzynski C. From a feedback-controlled demon to an information ratchet in a double quantum dot. Phys Rev E 2022; 106:064101. [PMID: 36671120 DOI: 10.1103/physreve.106.064101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2022] [Accepted: 11/15/2022] [Indexed: 06/17/2023]
Abstract
We present a simple strategy for constructing an information ratchet or memory-tape model of Maxwell's demon, from a feedback-controlled model. We illustrate our approach by converting the Annby-Andersson feedback-controlled double quantum dot model [Phys. Rev. B 101, 165404 (2020)2469-995010.1103/PhysRevB.101.165404] to a memory-tape model. We use the underlying network structure of the original model to design a set of bit interaction rules for the information ratchet. The new model is solved analytically in the limit of long interaction times. For finite-time interactions, semianalytical phase diagrams of operational modes are obtained. Stochastic simulations are used to verify theoretical results.
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Affiliation(s)
- Debankur Bhattacharyya
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - Christopher Jarzynski
- Institute for Physical Science and Technology, Department of Chemistry and Biochemistry, and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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5
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Penocchio E, Avanzini F, Esposito M. Information thermodynamics for deterministic chemical reaction networks. J Chem Phys 2022; 157:034110. [DOI: 10.1063/5.0094849] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
Information thermodynamics relates the rate of change of mutual information between two interacting subsystems to their thermodynamics when the joined system is described by a bipartite stochastic dynamics satisfying local detailed balance. Here, we expand the scope of information thermodynamics to deterministic bipartite chemical reaction networks, namely, composed of two coupled subnetworks sharing species but not reactions. We do so by introducing a meaningful notion of mutual information between different molecular features that we express in terms of deterministic concentrations. This allows us to formulate separate second laws for each subnetwork, which account for their energy and information exchanges, in complete analogy with stochastic systems. We then use our framework to investigate the working mechanisms of a model of chemically driven self-assembly and an experimental light-driven bimolecular motor. We show that both systems are constituted by two coupled subnetworks of chemical reactions. One subnetwork is maintained out of equilibrium by external reservoirs (chemostats or light sources) and powers the other via energy and information flows. In doing so, we clarify that the information flow is precisely the thermodynamic counterpart of an information ratchet mechanism only when no energy flow is involved.
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Affiliation(s)
- Emanuele Penocchio
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Francesco Avanzini
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
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6
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Wolpert DH. Strengthened second law for multi-dimensional systems coupled to multiple thermodynamic reservoirs. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20200428. [PMID: 35599569 PMCID: PMC9125225 DOI: 10.1098/rsta.2020.0428] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
The second law of thermodynamics can be formulated as a restriction on the evolution of the entropy of any system undergoing Markovian dynamics. Here I show that this form of the second law is strengthened for multi-dimensional, complex systems, coupled to multiple thermodynamic reservoirs, if we have a set of a priori constraints restricting how the dynamics of each coordinate can depend on the other coordinates. As an example, this strengthened second law (SSL) applies to complex systems composed of multiple physically separated, co-evolving subsystems, each identified as a coordinate of the overall system. In this example, the constraints concern how the dynamics of some subsystems are allowed to depend on the states of the other subsystems. Importantly, the SSL applies to such complex systems even if some of its subsystems can change state simultaneously, which is prohibited in a multipartite process. The SSL also strengthens previously derived bounds on how much work can be extracted from a system using feedback control, if the system is multi-dimensional. Importantly, the SSL does not require local detailed balance. So it potentially applies to complex systems ranging from interacting economic agents to co-evolving biological species. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.
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Affiliation(s)
- David H. Wolpert
- Santa Fe Institute, Santa Fe, NM, USA
- Complexity Science Hub, Vienna, Arizona State University, Tempe, AZ, USA
- International Center for Theoretical Physics, Italy
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7
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Wolpert DH. Strengthened second law for multi-dimensional systems coupled to multiple thermodynamic reservoirs. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022. [PMID: 35599569 DOI: 10.6084/m9.figshare.c.5896494] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
The second law of thermodynamics can be formulated as a restriction on the evolution of the entropy of any system undergoing Markovian dynamics. Here I show that this form of the second law is strengthened for multi-dimensional, complex systems, coupled to multiple thermodynamic reservoirs, if we have a set of a priori constraints restricting how the dynamics of each coordinate can depend on the other coordinates. As an example, this strengthened second law (SSL) applies to complex systems composed of multiple physically separated, co-evolving subsystems, each identified as a coordinate of the overall system. In this example, the constraints concern how the dynamics of some subsystems are allowed to depend on the states of the other subsystems. Importantly, the SSL applies to such complex systems even if some of its subsystems can change state simultaneously, which is prohibited in a multipartite process. The SSL also strengthens previously derived bounds on how much work can be extracted from a system using feedback control, if the system is multi-dimensional. Importantly, the SSL does not require local detailed balance. So it potentially applies to complex systems ranging from interacting economic agents to co-evolving biological species. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.
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Affiliation(s)
- David H Wolpert
- Santa Fe Institute, Santa Fe, NM, USA
- Complexity Science Hub, Vienna, Arizona State University, Tempe, AZ, USA
- International Center for Theoretical Physics, Italy
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8
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He L, Pradana A, Cheong JW, Chew LY. Information processing second law for an information ratchet with finite tape. Phys Rev E 2022; 105:054131. [PMID: 35706159 DOI: 10.1103/physreve.105.054131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2022] [Accepted: 05/03/2022] [Indexed: 06/15/2023]
Abstract
We model a class of discrete-time information ratchet with a finite tape and explore its thermodynamic consequence as a Maxwell demon. We found that, although it supports the operational regime of an engine or eraser, it cannot typically sustain these thermodynamic functionalities due to eventual equilibration as a result of the finite information capacity of the tape. Nonetheless, cumulative work can be accrued or expended through successive tape scans and we prove that at all time the ratchet obeys the information processing second law (IPSL). Unlike the IPSL for the infinite-tape ratchet which operates only at the stationary state, the IPSL here is applicable also at the transient phase of the ratchet operation. We explore two ratchet designs with the single-state perturbed coin (PC) ratchet being the simplest ratchet without memory, while the double-state modified Boyd's (MB) ratchet is the simplest ratchet with memory. Our analysis shows that the MB ratchet can harness correlation to accumulate more work by having a larger time constant to reach steady state relative to the PC ratchet.
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Affiliation(s)
- Lianjie He
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
| | - Andri Pradana
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
| | - Jian Wei Cheong
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
| | - Lock Yue Chew
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
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9
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Frank MP, Shukla K. Quantum Foundations of Classical Reversible Computing. ENTROPY (BASEL, SWITZERLAND) 2021; 23:701. [PMID: 34206044 PMCID: PMC8228632 DOI: 10.3390/e23060701] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/24/2021] [Revised: 05/24/2021] [Accepted: 05/27/2021] [Indexed: 11/16/2022]
Abstract
The reversible computation paradigm aims to provide a new foundation for general classical digital computing that is capable of circumventing the thermodynamic limits to the energy efficiency of the conventional, non-reversible digital paradigm. However, to date, the essential rationale for, and analysis of, classical reversible computing (RC) has not yet been expressed in terms that leverage the modern formal methods of non-equilibrium quantum thermodynamics (NEQT). In this paper, we begin developing an NEQT-based foundation for the physics of reversible computing. We use the framework of Gorini-Kossakowski-Sudarshan-Lindblad dynamics (a.k.a. Lindbladians) with multiple asymptotic states, incorporating recent results from resource theory, full counting statistics and stochastic thermodynamics. Important conclusions include that, as expected: (1) Landauer's Principle indeed sets a strict lower bound on entropy generation in traditional non-reversible architectures for deterministic computing machines when we account for the loss of correlations; and (2) implementations of the alternative reversible computation paradigm can potentially avoid such losses, and thereby circumvent the Landauer limit, potentially allowing the efficiency of future digital computing technologies to continue improving indefinitely. We also outline a research plan for identifying the fundamental minimum energy dissipation of reversible computing machines as a function of speed.
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Affiliation(s)
- Michael P. Frank
- Center for Computing Research, Sandia National Laboratories, Albuquerque, NM 87185, USA
| | - Karpur Shukla
- Department of Electrical and Computer Engineering, Brown University, Providence, RI 02906, USA
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10
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Wolpert DH. Uncertainty Relations and Fluctuation Theorems for Bayes Nets. PHYSICAL REVIEW LETTERS 2020; 125:200602. [PMID: 33258647 DOI: 10.1103/physrevlett.125.200602] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2020] [Revised: 06/30/2020] [Accepted: 09/11/2020] [Indexed: 05/10/2023]
Abstract
Recent research has considered the stochastic thermodynamics of multiple interacting systems, representing the overall system as a Bayes net. I derive fluctuation theorems governing the entropy production (EP) of arbitrary sets of the systems in such a Bayes net. I also derive "conditional" fluctuation theorems, governing the distribution of EP in one set of systems conditioned on the EP of a different set of systems. I then derive thermodynamic uncertainty relations relating the EP of the overall system to the precisions of probability currents within the individual systems.
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Affiliation(s)
- David H Wolpert
- Santa Fe Institute, Santa Fe, New Mexico Complexity Science Hub, Vienna Arizona State University, Tempe, Arizona 87501, USA
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11
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Diazdelacruz J. Quantum Relative Entropy of Tagging and Thermodynamics. ENTROPY 2020; 22:e22020138. [PMID: 33285913 PMCID: PMC7516547 DOI: 10.3390/e22020138] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/21/2019] [Revised: 01/10/2020] [Accepted: 01/22/2020] [Indexed: 11/22/2022]
Abstract
Thermodynamics establishes a relation between the work that can be obtained in a transformation of a physical system and its relative entropy with respect to the equilibrium state. It also describes how the bits of an informational reservoir can be traded for work using Heat Engines. Therefore, an indirect relation between the relative entropy and the informational bits is implied. From a different perspective, we define procedures to store information about the state of a physical system into a sequence of tagging qubits. Our labeling operations provide reversible ways of trading the relative entropy gained from the observation of a physical system for adequately initialized qubits, which are used to hold that information. After taking into account all the qubits involved, we reproduce the relations mentioned above between relative entropies of physical systems and the bits of information reservoirs. Some of them hold only under a restricted class of coding bases. The reason for it is that quantum states do not necessarily commute. However, we prove that it is always possible to find a basis (equivalent to the total angular momentum one) for which Thermodynamics and our labeling system yield the same relation.
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Affiliation(s)
- Jose Diazdelacruz
- Department of Applied Physics and Materials Engineering, Universidad Politecnica de Madrid, 28040 Madrid, Spain
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12
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Abstract
Biomolecular machines are protein complexes that convert between different forms of free energy. They are utilized in nature to accomplish many cellular tasks. As isothermal nonequilibrium stochastic objects at low Reynolds number, they face a distinct set of challenges compared with more familiar human-engineered macroscopic machines. Here we review central questions in their performance as free energy transducers, outline theoretical and modeling approaches to understand these questions, identify both physical limits on their operational characteristics and design principles for improving performance, and discuss emerging areas of research.
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Affiliation(s)
- Aidan I Brown
- Department of Physics , University of California, San Diego , La Jolla , California 92093 , United States
| | - David A Sivak
- Department of Physics , Simon Fraser University , Burnaby , British Columbia V5A 1S6 , Canada
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13
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Holeček M. Work as a memory record. Phys Rev E 2019; 99:062130. [PMID: 31330670 DOI: 10.1103/physreve.99.062130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2018] [Indexed: 11/07/2022]
Abstract
The possibility of a controlled manipulation with molecules at the nanoscale allows us to gain net work from thermal energy, although this seems to be in contradiction to the second law of thermodynamics. Any manipulation, however, causes some memory records somewhere in the system's surroundings. To complete the thermodynamic cycle, these records must be reset, which costs energy that cancels the previous gain. An important memory record may also be the final state of the work reservoir. This memory record is not reset. Nevertheless, it is rewritten and the associated memory erased whenever the state of the work reservoir is changed during the cycle repeating. The question is, what is the cost of this memory erasure. To answer it, we study a hypothetical cycle in which all memory records are reset except the state of the work reservoir alone, and the ensemble average of the work extracted from an equilibrium heat reservoir during this cycle, 〈W〉, is positive. It is shown that a strong information coupling of the system and the work reservoir then influences the system's dynamics so much that the cycle repeat may exhibit quite different behavior. Especially, it can run reversely and decrease energy in the work reservoir. It implies that even if the memory erasure is a natural part of the process, it costs energy in accord with information thermodynamics. At the nanoscale, this energy cost may manifest as a process obeying the fluctuation theorem.
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Affiliation(s)
- Miroslav Holeček
- New Technologies Research Center, University of West Bohemia, Plzeň 301 00, Czech Republic
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14
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Stevens J, Deffner S. Quantum to classical transition in an information ratchet. Phys Rev E 2019; 99:042129. [PMID: 31108656 DOI: 10.1103/physreve.99.042129] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2018] [Indexed: 11/07/2022]
Abstract
Recent years have seen a flurry of research activity in the study of minimal and autonomous information ratchets. However, the existing classical and quantum models are somewhat hard to compare and hence quantifying possible quantum supremacy in information ratchets has been elusive. We propose a step towards filling this void between quantum and classical ratchets by introducing a model with continuous variables: a quantum particle in a box coupled to a stream of qubits. The dynamics is solved exactly and we analyze the quantum to classical transition in terms of a natural timescale parameter for the model.
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Affiliation(s)
- Josey Stevens
- Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA.,Applied Physics Laboratory, Johns Hopkins University, Laurel, Maryland 20723, USA
| | - Sebastian Deffner
- Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA
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15
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Jinwoo L. Fluctuation Theorem of Information Exchange within an Ensemble of Paths Conditioned on Correlated-Microstates. ENTROPY 2019; 21:e21050477. [PMID: 33267191 PMCID: PMC7514966 DOI: 10.3390/e21050477] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/29/2019] [Revised: 05/02/2019] [Accepted: 05/06/2019] [Indexed: 11/16/2022]
Abstract
Fluctuation theorems are a class of equalities that express universal properties of the probability distribution of a fluctuating path functional such as heat, work or entropy production over an ensemble of trajectories during a non-equilibrium process with a well-defined initial distribution. Jinwoo and Tanaka (Jinwoo, L.; Tanaka, H. Sci. Rep.2015, 5, 7832) have shown that work fluctuation theorems hold even within an ensemble of paths to each state, making it clear that entropy and free energy of each microstate encode heat and work, respectively, within the conditioned set. Here we show that information that is characterized by the point-wise mutual information for each correlated state between two subsystems in a heat bath encodes the entropy production of the subsystems and heat bath during a coupling process. To this end, we extend the fluctuation theorem of information exchange (Sagawa, T.; Ueda, M. Phys. Rev. Lett.2012, 109, 180602) by showing that the fluctuation theorem holds even within an ensemble of paths that reach a correlated state during dynamic co-evolution of two subsystems.
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Affiliation(s)
- Lee Jinwoo
- Department of Mathematics, Kwangwoon University, 20 Kwangwoon-ro, Seoul 01897, Korea
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16
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Quantum Information Remote Carnot Engines and Voltage Transformers. ENTROPY 2019; 21:e21020127. [PMID: 33266843 PMCID: PMC7514606 DOI: 10.3390/e21020127] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/03/2019] [Revised: 01/24/2019] [Accepted: 01/28/2019] [Indexed: 11/17/2022]
Abstract
A physical system out of thermal equilibrium is a resource for obtaining useful work when a heat bath at some temperature is available. Information Heat Engines are the devices which generalize the Szilard cylinders and make use of the celebrated Maxwell demons to this end. In this paper, we consider a thermo-chemical reservoir of electrons which can be exchanged for entropy and work. Qubits are used as messengers between electron reservoirs to implement long-range voltage transformers with neither electrical nor magnetic interactions between the primary and secondary circuits. When they are at different temperatures, the transformers work according to Carnot cycles. A generalization is carried out to consider an electrical network where quantum techniques can furnish additional security.
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17
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Spinney RE, Prokopenko M, Chu D. Information ratchets exploiting spatially structured information reservoirs. Phys Rev E 2018; 98:022124. [PMID: 30253523 DOI: 10.1103/physreve.98.022124] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2017] [Indexed: 11/07/2022]
Abstract
Fully mechanized Maxwell's demons, also called information ratchets, are an important conceptual link between computation, information theory, and statistical physics. They exploit low-entropy information reservoirs to extract work from a heat reservoir. Previous models of such demons have either ignored the cost of delivering bits to the demon from the information reservoir or assumed random access or infinite-dimensional information reservoirs to avoid such an issue. In this work we account for this cost when exploiting information reservoirs with physical structure and show that the dimensionality of the reservoir has a significant impact on the performance and phase diagram of the demon. We find that for conventional one-dimensional tapes the scope for work extraction is greatly reduced. An expression for the net-extracted work by demons exploring information reservoirs by means of biased random walks on d-dimensional, Z^{d}, information reservoirs is presented. Furthermore, we derive exact probabilities of recurrence in these systems, generalizing previously known results. We find that the demon is characterized by two critical dimensions. First, to extract work at zero bias the dimensionality of the information reservoir must be larger than d=2, corresponding to the dimensions where a simple random walker is transient. Second, for integer dimensions d>4 the unbiased random walk optimizes work extraction corresponding to the dimensions where a simple random walker is strongly transient.
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Affiliation(s)
- Richard E Spinney
- Complex Systems Research Group and Centre for Complex Systems, The University of Sydney, Sydney, New South Wales 2006, Australia
| | - Mikhail Prokopenko
- Complex Systems Research Group and Centre for Complex Systems, The University of Sydney, Sydney, New South Wales 2006, Australia
| | - Dominique Chu
- School of Computing, University of Kent, Canterbury CT2 7NF, United Kingdom
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18
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Abstract
A central result of stochastic thermodynamics is that irreversible state transitions of Markovian systems entail a cost in terms of an infinite entropy production. A corollary of this is that strictly deterministic computation is not possible. Using a thermodynamically consistent model, we show that quasideterministic computation can be achieved at finite, and indeed modest cost with accuracies that are indistinguishable from deterministic behavior for all practical purposes. Concretely, we consider the entropy production of stochastic (Markovian) systems that behave like and and a not gates. Combinations of these gates can implement any logical function. We require that these gates return the correct result with a probability that is very close to 1, and additionally, that they do so within finite time. The central component of the model is a machine that can read and write binary tapes. We find that the error probability of the computation of these gates falls with the power of the system size, whereas the cost only increases linearly with the system size.
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Affiliation(s)
- Dominique Chu
- School of Computing, University of Kent, CT2 7NF, Canterbury, United Kingdom
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19
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Acconcia TV, Bonança MVS. Microcanonical Szilárd engines beyond the quasistatic regime. Phys Rev E 2017; 96:062117. [PMID: 29347443 DOI: 10.1103/physreve.96.062117] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2016] [Indexed: 11/07/2022]
Abstract
We discuss the possibility of extracting energy from a single thermal bath using microcanonical Szilárd engines operating in finite time. This extends previous works on the topic which are restricted to the quasistatic regime. The feedback protocol is implemented based on linear response predictions of the excess work. It is claimed that the underlying mechanism leading to energy extraction does not violate Liouville's theorem and preserves ergodicity throughout the cycle. We illustrate our results with several examples including an exactly solvable model.
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Affiliation(s)
- Thiago V Acconcia
- Instituto de Física "Gleb Wataghin," Universidade Estadual de Campinas, 777 Rua Sérgio Buarque de Holanda, Campinas, São Paulo 13083-859, Brazil
| | - Marcus V S Bonança
- Instituto de Física "Gleb Wataghin," Universidade Estadual de Campinas, 777 Rua Sérgio Buarque de Holanda, Campinas, São Paulo 13083-859, Brazil
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21
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Garner AJP, Thompson J, Vedral V, Gu M. Thermodynamics of complexity and pattern manipulation. Phys Rev E 2017; 95:042140. [PMID: 28505845 DOI: 10.1103/physreve.95.042140] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2016] [Indexed: 05/25/2023]
Abstract
Many organisms capitalize on their ability to predict the environment to maximize available free energy and reinvest this energy to create new complex structures. This functionality relies on the manipulation of patterns-temporally ordered sequences of data. Here, we propose a framework to describe pattern manipulators-devices that convert thermodynamic work to patterns or vice versa-and use them to build a "pattern engine" that facilitates a thermodynamic cycle of pattern creation and consumption. We show that the least heat dissipation is achieved by the provably simplest devices, the ones that exhibit desired operational behavior while maintaining the least internal memory. We derive the ultimate limits of this heat dissipation and show that it is generally nonzero and connected with the pattern's intrinsic crypticity-a complexity theoretic quantity that captures the puzzling difference between the amount of information the pattern's past behavior reveals about its future and the amount one needs to communicate about this past to optimally predict the future.
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Affiliation(s)
- Andrew J P Garner
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Jayne Thompson
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
| | - Vlatko Vedral
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
- Atomic and Laser Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
- Department of Physics, National University of Singapore, 3 Science Drive 2, Singapore 117543
| | - Mile Gu
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
- School of Physical and Mathematical Sciences, Nanyang Technological University, 639673, Singapore
- Complexity Institute, Nanyang Technological University, 639673, Singapore
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22
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Croucher T, Bedkihal S, Vaccaro JA. Discrete Fluctuations in Memory Erasure without Energy Cost. PHYSICAL REVIEW LETTERS 2017; 118:060602. [PMID: 28234546 DOI: 10.1103/physrevlett.118.060602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2016] [Indexed: 06/06/2023]
Abstract
According to Landauer's principle, erasing one bit of information incurs a minimum energy cost. Recently, Vaccaro and Barnett (VB) explored information erasure within the context of generalized Gibbs ensembles and demonstrated that for energy-degenerate spin reservoirs the cost of erasure can be solely in terms of a minimum amount of spin angular momentum and no energy. As opposed to the Landauer case, the cost of erasure in this case is associated with an intrinsically discrete degree of freedom. Here we study the discrete fluctuations in this cost and the probability of violation of the VB bound. We also obtain a Jarzynski-like equality for the VB erasure protocol. We find that the fluctuations below the VB bound are exponentially suppressed at a far greater rate and more tightly than for an equivalent Jarzynski expression for VB erasure. We expose a trade-off between the size of the fluctuations and the cost of erasure. We find that the discrete nature of the fluctuations is pronounced in the regime where reservoir spins are maximally polarized. We also state the first laws of thermodynamics corresponding to the conservation of spin angular momentum for this particular erasure protocol. Our work will be important for novel heat engines based on information erasure schemes that do not incur an energy cost.
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Affiliation(s)
- Toshio Croucher
- Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
| | - Salil Bedkihal
- Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
| | - Joan A Vaccaro
- Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
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23
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Loutchko D, Eisbach M, Mikhailov AS. Stochastic thermodynamics of a chemical nanomachine: The channeling enzyme tryptophan synthase. J Chem Phys 2017; 146:025101. [DOI: 10.1063/1.4973544] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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24
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Boyd AB, Mandal D, Crutchfield JP. Correlation-powered information engines and the thermodynamics of self-correction. Phys Rev E 2017; 95:012152. [PMID: 28208508 DOI: 10.1103/physreve.95.012152] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2016] [Indexed: 05/23/2023]
Abstract
Information engines can use structured environments as a resource to generate work by randomizing ordered inputs and leveraging the increased Shannon entropy to transfer energy from a thermal reservoir to a work reservoir. We give a broadly applicable expression for the work production of an information engine, generally modeled as a memoryful channel that communicates inputs to outputs as it interacts with an evolving environment. The expression establishes that an information engine must have more than one memory state in order to leverage input environment correlations. To emphasize this functioning, we designed an information engine powered solely by temporal correlations and not by statistical biases, as employed by previous engines. Key to this is the engine's ability to synchronize-the engine automatically returns to a desired dynamical phase when thrown into an unwanted, dissipative phase by corruptions in the input-that is, by unanticipated environmental fluctuations. This self-correcting mechanism is robust up to a critical level of corruption, beyond which the system fails to act as an engine. We give explicit analytical expressions for both work and critical corruption level and summarize engine performance via a thermodynamic-function phase diagram over engine control parameters. The results reveal a thermodynamic mechanism based on nonergodicity that underlies error correction as it operates to support resilient engineered and biological systems.
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Affiliation(s)
- Alexander B Boyd
- Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA
| | - Dibyendu Mandal
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - James P Crutchfield
- Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA
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25
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Yamamoto S, Ito S, Shiraishi N, Sagawa T. Linear irreversible thermodynamics and Onsager reciprocity for information-driven engines. Phys Rev E 2016; 94:052121. [PMID: 27967007 DOI: 10.1103/physreve.94.052121] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2016] [Indexed: 06/06/2023]
Abstract
In the recent progress in nonequilibrium thermodynamics, information has been recognized as a kind of thermodynamic resource that can drive thermodynamic current without any direct energy injection. In this paper, we establish the framework of linear irreversible thermodynamics for a broad class of autonomous information processing. In particular, we prove that the Onsager reciprocity holds true with information: The linear response matrix is well-defined and is shown symmetric with both of the information affinity and the conventional thermodynamic affinity. As an application, we derive a universal bound for the efficiency at maximum power for information-driven engines in the linear regime. Our result reveals the fundamental role of information flow in linear irreversible thermodynamics.
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Affiliation(s)
- Shumpei Yamamoto
- Department of Basic Science, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
| | - Sosuke Ito
- Department of Physics, Tokyo Institute of Technology, Oh-okayama 2-12-1, Meguro-ku, Tokyo 152-8551, Japan
| | - Naoto Shiraishi
- Department of Basic Science, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
| | - Takahiro Sagawa
- Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
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26
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Horowitz JM, Esposito M. Work producing reservoirs: Stochastic thermodynamics with generalized Gibbs ensembles. Phys Rev E 2016; 94:020102. [PMID: 27627226 DOI: 10.1103/physreve.94.020102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2016] [Indexed: 06/06/2023]
Abstract
We develop a consistent stochastic thermodynamics for environments composed of thermodynamic reservoirs in an external conservative force field, that is, environments described by the generalized or Gibbs canonical ensemble. We demonstrate that small systems weakly coupled to such reservoirs exchange both heat and work by verifying a local detailed balance relation for the induced stochastic dynamics. Based on this analysis, we help to rationalize the observation that nonthermal reservoirs can increase the efficiency of thermodynamic heat engines.
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Affiliation(s)
- Jordan M Horowitz
- Department of Physics, Physics of Living Systems Group, Massachusetts Institute of Technology, 400 Technology Square, Cambridge, Massachusetts 02139, USA
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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27
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The Free Energy Requirements of Biological Organisms; Implications for Evolution. ENTROPY 2016. [DOI: 10.3390/e18040138] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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28
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Hartich D, Barato AC, Seifert U. Sensory capacity: An information theoretical measure of the performance of a sensor. Phys Rev E 2016; 93:022116. [PMID: 26986297 DOI: 10.1103/physreve.93.022116] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2015] [Indexed: 05/10/2023]
Abstract
For a general sensory system following an external stochastic signal, we introduce the sensory capacity. This quantity characterizes the performance of a sensor: sensory capacity is maximal if the instantaneous state of the sensor has as much information about a signal as the whole time series of the sensor. We show that adding a memory to the sensor increases the sensory capacity. This increase quantifies the improvement of the sensor with the addition of the memory. Our results are obtained with the framework of stochastic thermodynamics of bipartite systems, which allows for the definition of an efficiency that relates the rate with which the sensor learns about the signal with the energy dissipated by the sensor, which is given by the thermodynamic entropy production. We demonstrate a general trade-off between sensory capacity and efficiency: if the sensory capacity is equal to its maximum 1, then the efficiency must be less than 1/2. As a physical realization of a sensor we consider a two-component cellular network estimating a fluctuating external ligand concentration as signal. This model leads to coupled linear Langevin equations that allow us to obtain explicit analytical results.
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Affiliation(s)
- David Hartich
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Andre C Barato
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
- Max Planck Institute for the Physics of Complex Systems, Nöthnizer Straße 38, 01187 Dresden, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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29
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Strasberg P, Cerrillo J, Schaller G, Brandes T. Thermodynamics of stochastic Turing machines. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042104. [PMID: 26565165 DOI: 10.1103/physreve.92.042104] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2015] [Indexed: 06/05/2023]
Abstract
In analogy to Brownian computers we explicitly show how to construct stochastic models which mimic the behavior of a general-purpose computer (a Turing machine). Our models are discrete state systems obeying a Markovian master equation, which are logically reversible and have a well-defined and consistent thermodynamic interpretation. The resulting master equation, which describes a simple one-step process on an enormously large state space, allows us to thoroughly investigate the thermodynamics of computation for this situation. Especially in the stationary regime we can well approximate the master equation by a simple Fokker-Planck equation in one dimension. We then show that the entropy production rate at steady state can be made arbitrarily small, but the total (integrated) entropy production is finite and grows logarithmically with the number of computational steps.
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Affiliation(s)
- Philipp Strasberg
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Javier Cerrillo
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Gernot Schaller
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Tobias Brandes
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
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