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1

An explanation of the Landauer bound and its ineffectiveness with regard to multivalued logic

Kycia Radosław A., Niemczynowcz Agnieszka

Technical Transactions

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2020

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Vol. 117, iss. 1

art. no. e2020042

EN

We discuss, using recent results on the thermodynamics of multivalued logic, the difficulties and pitfalls of how to apply the Landauer’s principle to thermodynamic computer memory models. The presentation is based on Szilard’s version of Maxwell’s demon experiment and use of equilibrium Thermodynamics. Different versions of thermodynamic/mechanical memory are presented – a one-hot encoding version and an implementation based on a reversed Szilard’s experiment. The relationship of the Landauer’s principle to the Galois connection is explained in detail.

PL

Opisujemy, używając niedawne badania związane z termodynamiką dla logiki wielowartościowej, problemy związane z zastosowaniem reguły Landauera dla termodynamicznego modelu pamięci komputera. Analiza jest oparta na wersji Szilarda demona Maxwella z termodynamiki równowagowej. Zostały zaprezentowane różne wersje termodynamicznej/mechanicznej pamięci – wersja gorąco jedynkowa i implementacja bazująca na odwróconym eksperymencie Szilarda. Zaprezentowano również związek pomiędzy regułą Landauera i koneksją Galois.

2

Obiegi termodynamiczne. Druga zasada termodynamiki

Litke B. J.

Problemy Nauk Stosowanych

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2018

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T. 8

91--98

PL

Wstęp i cele: W pracy opisano obieg termodynamiczny silnika cieplnego, Carnota, chłodziarki i pompy grzejnej, Ponadto przedstawiono sprawność termiczną obiegu silnika oraz sprawność energetyczną obiegu chłodniczego i obiegu grzejnego. Omówiono różne sformułowania drugiej zasady termodynamiki. Celem pracy jest przedstawienie graficzne obiegów termodynamicznych silnika, chłodziarki i pompy grzejnej oraz analiza teoretyczna sprawność energetycznej omawianych obiegów termodynamicznych. Materiał i metody: Materiał stanowią źródła z literatury z zakresu termodynamiki. W pracy zastosowano metodę analizy teoretycznej. Wyniki: Rezultatem pracy jest przedstawienie graficzne i omówienie obiegów termodynamicznych silnika cieplnego, chłodziarki i pompy grzejnej. Ponadto w pracy przestawiono analizę teoretyczną sprawności termicznej obiegu silnika, sprawności energetycznej obiegu chłodniczego i grzejnego. Wniosek: Aby zrealizować obieg silnika nie wystarczy tylko dostarczać ciepło, lecz konieczne jest też odprowadzanie ciepła. Obieg chłodniczy lub obieg grzejny jest lewobieżny i może składać się z równych przemian termodynamicznych. Sprawność termiczna silnika może być zwiększona poprzez podniesienie temperatury ciepła doprowadzanego i obniżenie temperatury ciepła odprowadzanego.

EN

Introduction and aim: The paper describes the thermodynamic cycle of the heat engine, Carnot, refrigeration and transient pump. In addition, the thermal efficiency of the motor cycle and the energy efficiency of the refrigeration cycle and heating circuit have been presented. Different definitions of the second law of thermodynamics have been discussed. The aim of this paper is graphic representation of thermodynamic cycles of the engine, refrigerator and heating pump as well as theoretical analysis of energy efficiency of the discussed thermodynamic cycles. Material and methods: Material covers some sources based on the literature in the field of thermodynamics. The method of theoretical analysis has been shown in the paper. Results: The result of the work is a graphic representation and discussion of the thermodynamic cycles of the heat engine, the refrigerator and the heating pump. In addition, the work presents the thermodynamic analysis of the thermal efficiency of the motor cycle, the energy efficiency of the cooling and heating circuits. Conclusion: In order to realize the motor cycle, it will not only provide heat, but also heat removal. The refrigeration circuit or heating circuit is left-handed and may consist of even thermodynamic transformations. The thermal efficiency of the motor can be increased by raising the temperature of the heat supplied and reducing the temperature of the heat dissipated.

3

The 2017 SNOOK PRIZES in Computational Statistical Mechanics

Hoover W. G., Hoover C. G.

Computational Methods in Science and Technology

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2018

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Vol. 24, No. 2

75--79

EN

The 2017 Snook Prize has been awarded to Kenichiro Aoki for his exploration of chaos in Hamiltonian 4 models. His work addresses symmetries, thermalization, and Lyapunov instabilities in few-particle dynamical systems. A companion paper by Timo Hofmann and Jochen Merker is devoted to the exploration of generalized Hénon-Heiles models and has been selected for Honorable Mention in the Snook-Prize competition.

4

Symmetry, Chaos and Temperature in the One-dimensional Lattice Φ4 Theory

Aoki K.

Computational Methods in Science and Technology

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2018

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Vol. 24, No. 2

83--95

EN

The symmetries of the minimal Φ4 theory on the lattice are systematically analyzed. We find that symmetry can restrict trajectories to subspaces, while their motions are still chaotic. The chaotic dynamics of autonomous Hamiltonian systems are discussed in relation to the thermodynamic laws. Possibilities of configurations with non-equal ideal gas temperatures in the steady state in Hamiltonian systems, are investigated, and examples of small systems in which the ideal gas temperatures are different within the system are found. The pairing of local (finite-time) Lyapunov exponents are analyzed, and their dependence on various factors, such as the energy of the system, the characteristics of the initial conditions are studied and discussed. We find that for the Φ4 theory, higher energies lead to faster pairing times. We also find that symmetries can impede the pairing of local Lyapunov exponents and the convergence of Lyapunov exponents.

5

Równoważność postulatu Plancka o nieodwracalności procesów przebiegających z tarciem i sformułowań drugiej zasady termodynamiki Clausiusa i Kelvina

Ziemba A.

Rudy i Metale Nieżelazne

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2008

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R. 53, nr 10

604-610

PL

Dwa klasyczne sformułowania drugiej zasady termodynamiki, Clausiusa i Kelvina [4], zostały przyjęte jako postulaty, będąc efektem kontynuacji pracy Carnota i uogólnienia wyników obserwacji procesów natury [1, 2]. Postulaty Plancka są takimi sformułowaniami drugiej zasady termodynamiki, których ważność można jednoznacznie zweryfikować na podstawie eksperymentów [3]. Postulaty przyjmuje się bez ścisłego dowodu, możliwe jest jednak dowodzenie ważności jednego sformułowania, po przyjęciu założenia o ważności dowolnego innego. Powszechnie znane są dowody równoważności sformułowań Kelvina i Clausiusa [4, 5], pierwszego i drugiego postulatu Plancka i sformułowania Kelvina [4], a także postulatów Plancka i sformułowania Kelvina [3]. W artykule zaproponowano dowody równoważności pierwszego postulatu Plancka, o nieodwracalności procesów przebiegających z tarciem, i sformułowań drugiej zasady termodynamiki Clausiusa i Kelvina. W dowodzie równoważności pierwszego postulatu Plancka i sformułowania Kelvina uwzględniono nie tylko ciepło tarcia mechanicznego, jak w dowodach przedstawionych w pracach [3, 4], lecz również ciepło tarcia wewnętrznego czynnika termodynamicznego. Pierwszy postulat Plancka może mieć zastosowanie do opisu i doskonalenia tych procesów technologicznych, w których tarcie odgrywa istotną rolę. Im więcej ciepła tarcia jest związane z procesem technologicznym, tym bardziej jest on odległy od wyidealizowanego pojęcia procesu odwracalnego. Szczególnie jest to widoczne w procesach przeróbki plastycznej i obróbki mechanicznej.

EN

Multiplicity of the second law of thermodynamics statements [6] points out on a universal occurrence of its phenomenological aspects in the processes appearing in the nature [7]. Two classical statements of the second law, Clausius' and Kelvin's statements [4], were accepted as the postulates, while being an effect of the Carnot's work continuation and generalization of results of the observation of the processes in the nature [1, 2]. The Planck's postulates are such second law statements, whose validity may be unequivocally verified by the experiments. Three Planck's postulates are directly connected with an essence of the second law, pointing out on a fact of the existence of the irreversible processes in the nature [3]. The postulates are taken as valid without strict proof; however it is possible to prove any one of the statements, if any of the others is accepted as a postulate. It means that all of the statements of the second law are equivalent, however it seems that more proofs of it cause the better understanding of the second law sense. Commonly well-known there are proofs of equivalence of the Kelvin's and the Clausius' statements [4, 5], the first and second Planck's postulates and the Kelvin's statement [4], also the Planck's postulates and the Kelvin's statement [3]. In this paper the equivalence of the first Planck's postulate, about irreversibility of the processes being proceeded with friction, and the Clausius' and the Kelvin's statements of the second law of thermodynamics are proposed. In the proof of equivalence of the first Planck's postulate and the Kelvin's statement not only heat coming from mechanical friction was taken into account, like in proofs presented in works [3, 4], but also heat coming from internal friction of a thermodynamical agent. The first Planck's postulate could be used to describe and optimize such technological processes, in which friction plays a significant role. The more heat coming from friction is accompanying the technological process, the more far it is from idealized concept of reversible process. Particularly it is noticed in the plastic working and machining processes.

6

Thermodynamical admissibility of Biot's model of poroelastic saturated materials

Wilmański K.

Archives of Mechanics

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2002

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Vol. 54, nr 5-6

709-736

EN

The paper is devoted to the analysis of nonlinear elastic two-component models of saturated porous media, which in a linear form, reproduce as closely as possible the classical Biot's model. We present a full evaluation of the second law of thermodynamics for four classes of nonlinear models. It is proven that two of them in which there is no dependence on higher gradients cannot lead to the Biot's model. On the other hand, two other models in which a dependence on the gradient of porosity is introduced, yield linear constitutive relations but not the field equations appearing in the Biot's model. However, a recombination of partial stresses and momentum sources leads to Biot's equations. This analysis together with earlier publications on the subject exhausts the discussion of the question of thermodynamical admissibility of the Biot's model.

7

Thermomechanically consistent formulations of the standard linear solid using fractional derivatives

Lion A.

Archives of Mechanics

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2001

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Vol. 53, nr 3

253-273

EN

We study the thermomechanical properties of a frequently used fractional generalisation of the standard linear solid. Its mathematical structure arises from an ordinary linear differential equation between stress and strain when replacing the first order time rates by fractional derivatives of the order .... If the parameters ... and ... are not further restricted, the model leads to an unphysical behaviour. In the case of harmonic deformations the dissipation modulus can become negative. This corresponds to a negative entropy production and violates the second law of thermodynamics. Then we propose two generalisations of the standard linear solid which are based on a so-called thermodynamically consistent fractional rheological element. It possesses a non-negative free energy and rate of dissipation for arbitrary deformation processes and is compatible with the second law of thermodynamics. The differential equations between stress and strain of the proposed generalisations contain also fractional derivatives of different orders but both the dynamic moduli and the relaxation spectra are non-negative functions of their arguments. No restrictions on the material parameters are required.