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Related papers: The physical limit of logical compare operation

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Using recently developed algorithms, we compute and compare best $L^2$ and $L^\infty$ rational approximations of analytic functions on the unit disk. Although there is some theory for these problems going back decades, this may be the first…

Numerical Analysis · Mathematics 2025-12-30 Michael S. Ackermann , Sean Reiter , Lloyd N. Trefethen

We revisit a fundamental result in real-time verification, namely that the binary reachability relation between configurations of a given timed automaton is definable in linear arithmetic over the integers and reals. In this paper we give a…

Logic in Computer Science · Computer Science 2017-04-20 Karin Quaas , Mahsa Shirmohammadi , James Worrell

We consider a simplified version of a solvable model by Mandal and Jarzynski, which constructively demonstrates the interplay between work extraction and the increase of the Shannon entropy of an information reservoir which is in contact…

Statistical Mechanics · Physics 2015-03-31 Neri Merhav

This paper talk about the complexity of computation by Turing Machine. I take attention to the relation of symmetry and order structure of the data, and I think about the limitation of computation time. First, I make general problem named…

Computational Complexity · Computer Science 2010-09-24 Koji Kobayashi

Irreversible information processing cannot be carried out without some inevitable thermodynamical work cost. This fundamental restriction, known as Landauer's principle, is increasingly relevant today, as the energy dissipation of computing…

Quantum Physics · Physics 2015-07-08 Philippe Faist , Frédéric Dupuis , Jonathan Oppenheim , Renato Renner

A precise definition for a quantum electron thermometer is given, as an electron reservoir coupled locally (e.g., by tunneling) to a sample, and brought into electrical and thermal equilibrium with it. A realistic model of a scanning…

Mesoscale and Nanoscale Physics · Physics 2013-05-08 Justin P. Bergfield , Shauna M. Story , Robert C. Stafford , Charles A. Stafford

Quantum operations provide a general description of the state changes allowed by quantum mechanics. The reversal of quantum operations is important for quantum error-correcting codes, teleportation, and reversing quantum measurements. We…

Quantum Physics · Physics 2009-10-30 M. A. Nielsen , Carlton M. Caves , Benjamin Schumacher , Howard Barnum

Quantum complexity measures the difficulty of realizing a quantum process, such as preparing a state or implementing a unitary. We present an approach to quantifying the thermodynamic resources required to implement a process if the…

Most modal logics such as S5, LTL, or ATL are extensions of Modal Logic K. While the model checking problems for LTL and to a lesser extent ATL have been very active research areas for the past decades, the model checking problem for the…

Artificial Intelligence · Computer Science 2012-07-11 Abdallah Saffidine

As revealed by discussions of principle on energy dissipation by computers, logic imposes constraints on physical systems designed for a logical function. We define a notion of logical dissipation for a finite automaton. We discuss the…

Quantum Physics · Physics 2007-05-23 Philippe Matherat , Marc-Thierry Jaekel

We present a very simple method for the calculation of Shannon, Fisher, Onicescu and Tsallis entropies in atoms, as well as SDL and LMC complexity measures, as functions of the atomic number Z. Fractional occupation probabilities of…

Quantum Physics · Physics 2015-05-13 C. P. Panos , N. S. Nikolaidis , K. Ch. Chatzisavvas , C. C. Tsouros

Questioning the presumably most basic assumptions about the structure of space and time has revolutionized our understanding of Nature. State-of-the-art atomic clocks make it possible to precisely test fundamental symmetry properties of…

In Szilard's engine, measurement and feedback allows to extract work from an equilibrium environment, a process otherwise forbidden by the laws of thermodynamics. Recent theoretical developments have established fluctuation theorems and…

Mesoscale and Nanoscale Physics · Physics 2025-11-14 David Barker , Sebastian Lehmann , Kimberly A. Dick , Peter Samuelsson , Ville Maisi , Patrick P. Potts

Whilst the complexity of acquiring knowledge of a quantum state has been extensively studied in the fields of quantum tomography and quantum learning, a physical understanding of its operational role and cost in quantum thermodynamics is…

Quantum Physics · Physics 2025-11-06 Jake Xuereb , A. de Oliveira Junior , Fabien Clivaz , Pharnam Bakhshinezhad , Marcus Huber

The accuracy and complexity of machine learning algorithms based on kernel optimization are limited by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…

Machine Learning · Computer Science 2020-06-16 Brendon K. Colbert , Matthew M. Peet

In this theoretical study, we determine the maximum amount of work extractable in finite time by a demon performing continuous measurements on a quadratic Hamiltonian system subjected to thermal fluctuations, in terms of the information…

Statistical Mechanics · Physics 2014-10-21 Henrik Sandberg , Jean-Charles Delvenne , Nigel J. Newton , Sanjoy K. Mitter

A neat 1972 result of Pohl asserts that [3n/2]-2 comparisons are sufficient, and also necessary in the worst case, for finding both the minimum and the maximum of an n-element totally ordered set. The set is accessed via an oracle for…

Data Structures and Algorithms · Computer Science 2015-05-18 Michael Hoffmann , Jiří Matoušek , Yoshio Okamoto , Philipp Zumstein

We consider the optimization variant of the realizability problem for Prompt Linear Temporal Logic, an extension of Linear Temporal Logic (LTL) by the prompt eventually operator whose scope is bounded by some parameter. In the realizability…

Logic in Computer Science · Computer Science 2016-09-15 Leander Tentrup , Alexander Weinert , Martin Zimmermann

The second law of thermodynamics dictates the fundamental limits to the amount of energy and information that can be exchanged between physical systems. In this work, we extend a thermodynamic formalism describing this flow of energy and…

Statistical Mechanics · Physics 2015-03-24 Jordan M. Horowitz

Among the approximation methods for the verification of counter systems, one of them consists in model-checking their flat unfoldings. Unfortunately, the complexity characterization of model-checking problems for such operational models is…

Logic in Computer Science · Computer Science 2013-04-24 Stéphane Demri , Amit Kumar Dhar , Arnaud Sangnier