Zur phänomenologischen Begründung erweiterter Casimir-Onsagerscher Reziprozitätsbeziehungen (Diskussion der Voraussetzungen)

1969 ◽  
Vol 24 (6) ◽  
pp. 876-882
Author(s):  
W. Muschik
Keyword(s):  
Time Reversal ◽  
Linear Case ◽  
Reciprocal Relations ◽  
Main Assumption ◽  
Parameter Inversion ◽  
Non Linear ◽  
Onsager Reciprocal Relations

The conditions sufficient for a phenomenological derivation of non-linear Casimir-Onsager reciprocal relations are restated and discussed. The main assumption is that systems can be combined without restriction. The time-reversal is identified with the parameter-inversion of the thermodynamical forces. In a supplement non-linear reciprocal relations are expanded in components, and their validity is shown for the non-linear case if the forces depend on each other.

Zur phänomenologischen Begründung erweiterter Casimir-Onsagerscher Reziprozitätsbeziehungen

1968 ◽  
Vol 23 (10) ◽  
pp. 1446-1451 ◽  
Author(s):  
W. Muschik
Keyword(s):  
Time Reversal ◽  
State Variables ◽  
Balance Equations ◽  
Reciprocal Relations ◽  
First Time ◽  
Onsager Reciprocal Relations

Attempts are made to give phenomenological reasons for nonlinear Casimir-Onsager reciprocal relations. The fluxes can be defined as time derivations of state variables, or they can be explained by means of balance equations, because only their vectorial properties are used. At first, time reversal is replaced by an abstract parameter reversal from which involutoric transformations of forces and fluxes result. The connection between the parameter reversal of forces and fluxes allows to give reasons for relations which are equal to the Casimir-Onsager reciprocal relations apart from a sign. This sign is determined by experience. The connection between parameter and time reversal is discussed.

scholarly journals Onsager reciprocal relations with broken time-reversal symmetry

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Rongxiang Luo ◽  
Giuliano Benenti ◽  
Giulio Casati ◽  
Jiao Wang
Keyword(s):  
Time Reversal ◽  
Time Reversal Symmetry ◽  
Reciprocal Relations ◽  
Onsager Reciprocal Relations

scholarly journals Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic Fields

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1336 ◽  
Author(s):  
Davide Carbone ◽  
Lamberto Rondoni
Keyword(s):  
Magnetic Field ◽  
Statistical Mechanics ◽  
Time Reversal ◽  
Sufficient Conditions ◽  
Reciprocal Relations ◽  
Long Time ◽  
Necessary And Sufficient ◽  
Generalized Time ◽  
The Magnetic Field ◽  
Onsager Reciprocal Relations

Time reversal invariance (TRI) of particles systems has many consequences, among which the celebrated Onsager reciprocal relations, a milestone in Statistical Mechanics dating back to 1931. Because for a long time it was believed that (TRI) dos not hold in presence of a magnetic field, a modification of such relations was proposed by Casimir in 1945. Only in the last decade, the strict traditional notion of reversibility that led to Casimir’s work has been questioned. It was then found that other symmetries can be used, which allow the Onsager reciprocal relations to hold without modification. In this paper we advance this investigation for classical Hamiltonian systems, substantially increasing the number of symmetries that yield TRI in presence of a magnetic field. We first deduce the most general form of a generalized time reversal operation on the phase space of such a system; secondly, we express sufficient conditions on the magnetic field which ensure TRI. Finally, we examine common examples from statistical mechanics and molecular dynamics. Our main result is that TRI holds in a much wider generality than previously believed, partially explaining why no experimental violation of Onsager relations has so far been reported.

scholarly journals Ensemble variational assimilation as a probabilistic estimator – Part 1: The linear and weak non-linear case

2018 ◽  
Vol 25 (3) ◽  
pp. 565-587 ◽  
Author(s):  
Mohamed Jardak ◽  
Olivier Talagrand
Keyword(s):  
Probability Distribution ◽  
Simple Procedure ◽  
Linear Case ◽  
Bayesian Probability ◽  
Variational Assimilation ◽  
Non Linear ◽  
Abstract Data ◽  
Gaussian Case ◽  
Low Dimensional ◽  
Lorenz 96

Abstract. Data assimilation is considered as a problem in Bayesian estimation, viz. determine the probability distribution for the state of the observed system, conditioned by the available data. In the linear and additive Gaussian case, a Monte Carlo sample of the Bayesian probability distribution (which is Gaussian and known explicitly) can be obtained by a simple procedure: perturb the data according to the probability distribution of their own errors, and perform an assimilation on the perturbed data. The performance of that approach, called here ensemble variational assimilation (EnsVAR), also known as ensemble of data assimilations (EDA), is studied in this two-part paper on the non-linear low-dimensional Lorenz-96 chaotic system, with the assimilation being performed by the standard variational procedure. In this first part, EnsVAR is implemented first, for reference, in a linear and Gaussian case, and then in a weakly non-linear case (assimilation over 5 days of the system). The performances of the algorithm, considered either as a probabilistic or a deterministic estimator, are very similar in the two cases. Additional comparison shows that the performance of EnsVAR is better, both in the assimilation and forecast phases, than that of standard algorithms for the ensemble Kalman filter (EnKF) and particle filter (PF), although at a higher cost. Globally similar results are obtained with the Kuramoto–Sivashinsky (K–S) equation.

The Coupling Effect of Driving Forces to the Anti-Gravity Flow in the Spiral Micro-Channel

2011 ◽  
Author(s):  
Yan Li ◽  
Shuchao Zhang ◽  
Ning Mei
Keyword(s):  
Driving Force ◽  
Driving Forces ◽  
Coupling Effect ◽  
Three Dimensional ◽  
Horizontal Tube ◽  
Gravity Flow ◽  
Micro Channel ◽  
Reciprocal Relations ◽  
Coupling Relationship ◽  
Onsager Reciprocal Relations

In this paper, the anti-gravity flow in the spiral micro-channel on the surface of horizontal tube was visualized by the three-dimensional ultra-microscope system. The coupling relationship between the driving force and the flow was studied by Onsager reciprocal relations. The results show that the formation of the anti-gravity flow in the spiral micro-channel on the surface of horizontal tube is impacted by the combining effect of several factors, such as the capillary pressure, wettability, temperature, and bubbles.

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