Cl35(d, p)Cl36 in the unified model

Mehta, M.L.; Warke, C. S.

doi:10.1016/0029-5582(59)90122-1

Cited by 9 publications

(9 citation statements)

References 4 publications

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“…I will also not consider the (copious) literature on the thermodynamics of biochemical processes in cells that can be viewed as noisy types of information processing. (See [33][34][35][36][37][38][39] for some work on this topic.) The key criterion for including some literature in the current paper is whether it concerns thermodynamic properties of one of the types of computational machine considered in the computer science literature.…”

Section: Topics Not Covered In This Papermentioning

confidence: 99%

“…In this subsection I summarize the answer to this question originally given in [62]. 39 . First, in order to avoid the problems that arise if we only sum entropic costs incurred by running a system 38 In general, that set is infinite, since for any input string i that causes the UTM to compute o, we can construct another input string that just loops an arbitrary number of times, doing nothing, before it runs the computation starting from i.…”

Section: Kolmogorov Complexity and The Entropy Dynamics Of Turinmentioning

confidence: 99%

“…First, in order to avoid the problems that arise if we only sum entropic costs incurred by running a system 38 In general, that set is infinite, since for any input string i that causes the UTM to compute o, we can construct another input string that just loops an arbitrary number of times, doing nothing, before it runs the computation starting from i. 39 [62] considered conventional three-tape implementations of prefix TMs rather than single tape implementations.…”

Section: Kolmogorov Complexity and The Entropy Dynamics Of Turinmentioning

confidence: 99%

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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: Topics Not Covered In This Papermentioning

confidence: 99%

Section: Kolmogorov Complexity and The Entropy Dynamics Of Turinmentioning

confidence: 99%

Section: Kolmogorov Complexity and The Entropy Dynamics Of Turinmentioning

confidence: 99%

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The stochastic thermodynamics of computation

Wolpert¹

2019

J. Phys. A: Math. Theor.

139

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“…Examples of this are e.g. the relations between neural networks and statistical Ising models and renormalisation flow [9], the use of tensor network techniques to train them [10], and indeed the very concept of phase transitions themselves [11].…”

Section: Introductionmentioning

confidence: 99%

Learning phase transitions by confusion

2017

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Classifying phases of matter is key to our understanding of many problems in physics. For quantum-mechanical systems in particular, the task can be daunting due to the exponentially large Hilbert space. With modern computing power and access to ever-larger data sets, classification problems are now routinely solved using machine-learning techniques 1 . Here, we propose a neural-network approach to finding phase transitions, based on the performance of a neural network after it is trained with data that are deliberately labelled incorrectly. We demonstrate the success of this method on the topological phase transition in the Kitaev chain 2 , the thermal phase transition in the classical Ising model 3 , and the many-body-localization transition in a disordered quantum spin chain 4 . Our method does not depend on order parameters, knowledge of the topological content of the phases, or any other specifics of the transition at hand. It therefore paves the way to the development of a generic tool for identifying unexplored phase transitions.Machine learning as a tool for analysing data is becoming more and more prevalent in an increasing number of fields. This is due to a combination of availability of large amounts of data and the advances in hardware and computational power, the latter most notably through the use of graphical processing units.Two typical methods of machine learning can be distinguished, namely the unsupervised and supervised methods. In the former the machine receives no input other than the data and is asked, for example, to extract features or to cluster the samples. Such an unsupervised approach was applied to identify phase transitions and order parameters from images of classical configurations of Ising models 5 . In the supervised learning methods, the data have to be supplemented by a set of labels. A typical example is classification of data, where each sample is assigned a class label. The machine is trained to recognize samples and predict their associated label, demonstrating that it has learned by generalizing to samples it has not encountered before. This approach, too, has been demonstrated on Ising models Motivated by previous studies, we apply machine-learning techniques to the detection of phase transitions. In contrast to the earlier works, however, we focus on a combination of supervised and unsupervised techniques. In most cases, namely, it is exactly the labelling that one would like to find out (that is, classification of phases). That implies that a labelling is not known beforehand, and hence supervised techniques are not directly applicable. In this Letter we demonstrate that it is possible to find the correct labels, by purposefully mislabelling the data and evaluating the performance of the machine learner. We will base our method on NNs, which are capable of fitting arbitrary nonlinear functions 11 . Indeed, if a linear feature extraction method worked, there would have been no need to explicitly find labels in the first place.We emphasize the main result in this work is...

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“…Because it was not clear whether the antibodies produced within and outside the CNS are derived from the same clones, we compared the profiles of measles specific IgG eluted from matching pairs of CSF and serum from SSPE patients. 18 The data showed that measles-specific bands in CSF and serum in pH region 8.5 to 9.3 showed identical band patterns with respect to number, intensity, isoelectric point and light chain class. The data indicated that the same cell clones are responsible for the synthesis of the bands in the CNS and serum of patients with SSPE.…”

Section: Measles Virus Antibodies and Oligoclonal Bandsmentioning

confidence: 88%