scholarly journals Entropy Derived from Causality

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 647
Author(s):  
Roland Riek
Keyword(s):  
Discrete Time ◽  
Second Law Of Thermodynamics ◽  
Small Time ◽  
Second Law ◽  
Time Interval ◽  
Arrow Of Time ◽  
Mathematical Relationship ◽  
Time Step ◽  
Classical Physics ◽  
Small Time Step

The second law of thermodynamics, with its positive change of entropy for a system not in equilibrium, defines an arrow of time. Interestingly, also, causality, which is the connection between a cause and an effect, requests a direction of time by definition. It is noted that no other standard physical theories show this property. It is the attempt of this work to connect causality with entropy, which is possible by defining time as the metric of causality. Under this consideration that time appears only through a cause–effect relationship (“measured”, typically, in an apparatus called clock), it is demonstrated that time must be discrete in nature and cannot be continuous as assumed in all standard theories of physics including general and special relativity, and classical physics. The following lines of reasoning include: (i) (mechanical) causality requests that the cause must precede its effect (i.e., antecedence) requesting a discrete time interval >0. (ii) An infinitely small time step d t > 0 is thereby not sufficient to distinguish between cause and effect as a mathematical relationship between the two (i.e., Poisson bracket) will commute at a time interval d t , while not evidently within discrete time steps Δ t . As a consequence of a discrete time, entropy emerges (Riek, 2014) connecting causality and entropy to each other.

Load Discontinuity and Its Remedy in Step-by-Step Integration

2006 ◽  
Author(s):  
Shuenn-Yih Chang ◽  
Chiu-Li Huang
Keyword(s):  
Numerical Solution ◽  
Small Time ◽  
Step Size ◽  
Time Step ◽  
Integration Procedure ◽  
Amplitude Distortion ◽  
Small Time Step

The discontinuity at the end of an impulse will lead to an extra impulse and thus an extra displacement. Consequently, an amplitude distortion is introduced in the numerical solution. The difficulty arising from the discontinuity at the end of an impulse can be overcome by using a very small time step to perform the step-by-step integration since it reduces the extra impulse and thus extra displacement. However, computational efforts might be significantly increased since the small time step is performed for a complete step-by-step integration procedure. A remedy is devised to computationally efficiently overcome this difficulty by using a very small time step immediately upon termination of the applied impulse. This is because that the extra impulse caused by the discontinuity is almost proportional to the discontinuity value at the end of the impulse and the step size. The feasibility of this proposed remedy is analytically and numerically confirmed herein.

Simulation of Red Blood Cell Passing Through Constrictions Using Modified Moving Particle Semi-Implicit Method

2011 ◽  
Author(s):  
K. Firoozbakhsh ◽  
M. T. Ahmadian ◽  
M. Hasanian
Keyword(s):  
Mechanical Behavior ◽  
Experimental Studies ◽  
Small Time ◽  
Implicit Method ◽  
Parallel Plates ◽  
Time Step ◽  
Mps Method ◽  
Time Step Size ◽  
Small Time Step ◽  
Moving Particle

During the circulation of RBC it undergoes elastic deformation as it passes through micro-capillaries where the inner diameter of the constriction can be about 3 micro meters. It means RBC shape must be changed in order to pass through these narrow channels. The role of mechanical behavior of RBC and the deformability traits of RBC are observed with the several experimental studies [1]. Several methods were implemented to simulate the mechanical behavior of RBCs in micro-capillaries [1, 2]. One of the most recent methods is Moving Particle Semi-implicit method (MPS) which is a Lagrangian method with semi-implicit algorithm that guaranties the incompressibility of the fluid. MPS method was implemented for simulation of RBC motion through parallel plates by Tsubota et al. 2006 [3]. Due to small Reynolds number and the Diffusion number restrictions, implementation of small time step size would be necessary which leads to long time simulation. By the way in case of complex geometries or FSI problems, standard MPS method has a delicate pressure solver which leads to diverge the solution. So in these cases using a small time step can help to overcome the problem. Some studies have applied a new approach for time integration and the fractional time step method is employed to overcome the noticed problem. Yohsuke Imai and coworkers (2010) have developed the former studies with two main new approaches [4]. Firstly, evaluation of viscosity is upgraded and secondly boundary condition is assumed to be periodic. Although the developments are really impressive and MPS method has turned into a practical method for simulation of RBC motion in micro-capillaries, but still there are some considerations about using large time steps and error of the velocity profile consequently.

scholarly journals A diffusion Monte Carlo algorithm with very small time‐step errors

1993 ◽  
Vol 99 (4) ◽  
pp. 2865-2890 ◽  
Author(s):  
C. J. Umrigar ◽  
M. P. Nightingale ◽  
K. J. Runge
Keyword(s):  
Monte Carlo ◽  
Small Time ◽  
Monte Carlo Algorithm ◽  
Diffusion Monte Carlo ◽  
Time Step ◽  
Small Time Step

Stability Analysis Research of Modified CD-Newmark Numerical Integral Method in Seismic Pseudo-Dynamic Test

2014 ◽  
Vol 638-640 ◽  
pp. 1869-1872
Author(s):  
Xin Jiang Cai ◽  
Shi Zhu Tian
Keyword(s):  
Integral Method ◽  
Dynamic Test ◽  
Stable Condition ◽  
Small Time ◽  
Stability Conditions ◽  
Newmark Method ◽  
Time Step ◽  
Unconditionally Stable ◽  
Small Time Step ◽  
Numerical Integral

The characteristics of explicit numerical integral method is without iteration, and the characteristics of inexplicit numerical integral method is unconditionally stable. The traditional CD-Newmark method has the shortcoming of the bigger upper frequency leads to a small time step, a modified combined integral method named MCD-Newmark release the fixed DOF of numerical substructure, then obtained the parameters range of stable condition of experimental substructure, and the unconditionally stable of numerical substructure is also researched,then the strict stability conditions of the traditional CD-Newmark algorithm is resolved. The study provides reference for structural seismic test.

A Scientific Reading of Levinas’ Response to Heidegger: The Redemptive Edge of Time

KronoScope ◽  
2012 ◽  
Vol 12 (1) ◽  
pp. 73-89
Author(s):  
David Grandy
Keyword(s):  
Nineteenth Century ◽  
Martin Heidegger ◽  
Emmanuel Levinas ◽  
Physical Science ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Arrow Of Time ◽  
Self Identity ◽  
Heat Death

AbstractIn responding to Martin Heidegger, Emmanuel Levinas characterized time as revelatory and redemptive. For Levinas, Heideggerian being was self-contained and self-identical, and therefore unable to generate the sense of novel possibility which occasions the fleeting present. Something similar to Heideggerian Being may be said to have taken hold in the nineteenth century with the development of thermodynamics. The second law of thermodynamics was portrayed as the “arrow of time” moving inevitably toward universal heat death—cosmic stasis or self-identity. I argue that modern physical science itself does not fully validate this portrayal. There are, at the metaphysical level, explanatory gaps or openings which suggest other, more hopeful possibilities. These openings, I submit, are analogous to the ruptures of otherness which Levinas identified with the generosity of being and time’s redemptive aspect.

scholarly journals Convergence Improved Lax-Friedrichs Scheme Based Numerical Schemes and Their Applications in Solving the One-Layer and Two-Layer Shallow-Water Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Xinhua Lu ◽  
Bingjiang Dong ◽  
Bing Mao ◽  
Xiaofeng Zhang
Keyword(s):  
High Resolution ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Small Time ◽  
Numerical Schemes ◽  
Time Step ◽  
Numerical Diffusion ◽  
First Order ◽  
Small Time Step ◽  
The One

The first-order Lax-Friedrichs (LF) scheme is commonly used in conjunction with other schemes to achieve monotone and stable properties with lower numerical diffusion. Nevertheless, the LF scheme and the schemes devised based on it, for example, the first-order centered (FORCE) and the slope-limited centered (SLIC) schemes, cannot achieve a time-step-independence solution due to the excessive numerical diffusion at a small time step. In this work, two time-step-convergence improved schemes, the C-FORCE and C-SLIC schemes, are proposed to resolve this problem. The performance of the proposed schemes is validated in solving the one-layer and two-layer shallow-water equations, verifying their capabilities in attaining time-step-independence solutions and showing robustness of them in resolving discontinuities with high-resolution.

Thermodynamic Modeling for Discrete-Time Large-Scale Dynamical Systems

2011 ◽  
Author(s):  
Wassim M. Haddad ◽  
Sergey G. Nersesov
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Thermodynamic Modeling ◽  
Discrete Time ◽  
Large Scale ◽  
Type Inequality ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Thermodynamic Models ◽  
Definition Of

This chapter describes the thermodynamic modeling of discrete-time large-scale dynamical systems. In particular, it develops nonlinear discrete-time compartmental models that are consistent with thermodynamic principles. Since thermodynamic models are concerned with energy flow among subsystems, the chapter constructs a nonlinear compartmental dynamical system model characterized by conservation of energy and the first law of thermodynamics. It then provides a deterministic definition of entropy for a large-scale dynamical system that is consistent with the classical thermodynamic definition of entropy and shows that it satisfies a Clausius-type inequality leading to the law of entropy nonconservation. The chapter also considers nonconservation of entropy and the second law of thermodynamics, nonconservation of ectropy, semistability of discrete-time thermodynamic models, entropy increase and the second law of thermodynamics, and thermodynamic models with linear energy exchange.

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