scholarly journals The Principle of Least Action for Reversible Thermodynamic Processes and Cycles

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 542 ◽  
Author(s):  
Tian Zhao ◽  
Yu-Chao Hua ◽  
Zeng-Yuan Guo
Keyword(s):  
Heat Release ◽  
Optimization Problems ◽  
Optimal Path ◽  
Classical Mechanics ◽  
Carnot Cycle ◽  
Heat Absorption ◽  
Least Action ◽  
Principle Of Least Action ◽  
Thermodynamic Processes ◽  
Release Processes

The principle of least action, which is usually applied to natural phenomena, can also be used in optimization problems with manual intervention. Following a brief introduction to the brachistochrone problem in classical mechanics, the principle of least action was applied to the optimization of reversible thermodynamic processes and cycles in this study. Analyses indicated that the entropy variation per unit of heat exchanged is the mode of action for reversible heat absorption or heat release processes. Minimizing this action led to the optimization of heat absorption or heat release processes, and the corresponding optimal path was the first or second half of a Carnot cycle. Finally, the action of an entire reversible thermodynamic cycle was determined as the sum of the actions of the heat absorption and release processes. Minimizing this action led to a Carnot cycle. This implies that the Carnot cycle can also be derived using the principle of least action derived from the entropy concept.

scholarly journals Comments on “The Principle of Least Action for Reversible Thermodynamic Processes and Cycles”, Entropy 2018, 20, 542

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 980 ◽  
Author(s):  
Edward Bormashenko
Keyword(s):  
Variational Problem ◽  
Heat Generation ◽  
Carnot Cycle ◽  
Transversality Conditions ◽  
Rectangular Shape ◽  
Least Action ◽  
Principle Of Least Action ◽  
Thermodynamic Processes

The goal of this comment note is to express my concerns about the recent paper by Tian Zhao et al. (Entropy 2018, 20, 542). It is foreseen that this comment will stimulate a fruitful discussion of the issues involved. The principle of the least thermodynamic action is applicable for the analysis of the Carnot cycle using the entropy (not heat) generation extrema theorem. The transversality conditions of the variational problem provide the rectangular shape of the ST diagram for the Carnot cycle.

scholarly journals A least action principle for interceptive walking

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun Chae Chung ◽  
MooYoung Choi
Keyword(s):  
Social Systems ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Action Principle ◽  
Lagrange Equations ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Human Participants

AbstractThe principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

scholarly journals Action in Economics: Mathematical Derivation of Laws of Economics from the Principle of Least Action in Physics

2021 ◽  
Author(s):  
Sayan Kombarov
Keyword(s):  
Mathematical Formulation ◽  
Classical Mechanics ◽  
Human Action ◽  
Fundamental Principle ◽  
Austrian School ◽  
Rate Theory ◽  
Main Stream ◽  
Marginal Value ◽  
Least Action ◽  
Principle Of Least Action

The thesis of this paper is mathematical formulation of the laws of Economics with application of the principle of Least Action of classical mechanics. This paper is proposed as the rigorous mathematical approach to Economics provided by the fundamental principle of the physical science – the Principle of Least Action. This approach introduces the principle of Action into main-stream economics and allows reconcile main principles Austrian School of Economics and the laws of market, such Say’s law and marginal value and interest rate theory, with the modern results of mathematical economics, such as Capital Asset Pricing Model (CAPM), game theory and behavioral economics. This principle is well known in classical mechanics as the law of conservation of action that governs any system as a whole and all its components. It led to the revolution in physics, as it allows to derive the laws of Newtonian and quantum mechanics and probability. Ludwig von Mises defined Economics is the science of Human Action. Action is introduced into Economics by the founder of Austrian School of Economic, Carl Menger. Production or acquisition of any goods, services and assets are results of purposeful acts in the form of expenditure of work and energy in the form of flow of money and material resources. Humans take them to achieve certain desired goals with given resources and time. Any economic good and service, financial, productive, or real estate asset is the result of such action.

scholarly journals Extended harmonic mapping connects the equations in classical, statistical, fluid, quantum physics and general relativity

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Xiaobo Zhai ◽  
Changyu Huang ◽  
Gang Ren
Keyword(s):  
General Relativity ◽  
Quantum Physics ◽  
Harmonic Maps ◽  
Classical Mechanics ◽  
Harmonic Mapping ◽  
Geodesic Equation ◽  
Lagrange Equations ◽  
Least Action ◽  
Principle Of Least Action ◽  
Fundamental Equations

Abstract One potential pathway to find an ultimate rule governing our universe is to hunt for a connection among the fundamental equations in physics. Recently, Ren et al. reported that the harmonic maps with potential introduced by Duan, named extended harmonic mapping (EHM), connect the equations of general relativity, chaos and quantum mechanics via a universal geodesic equation. The equation, expressed as Euler–Lagrange equations on the Riemannian manifold, was obtained from the principle of least action. Here, we further demonstrate that more than ten fundamental equations, including that  of classical mechanics, fluid physics, statistical physics, astrophysics, quantum physics and general relativity, can be connected by the same universal geodesic equation. The connection sketches a family tree of the physics equations, and their intrinsic connections reflect an alternative ultimate rule of our universe, i.e., the principle of least action on a Finsler manifold.

The whole of physics

2017 ◽  
Author(s):  
Jennifer Coopersmith
Keyword(s):  
Physical Chemistry ◽  
General Relativity ◽  
Electromagnetic Waves ◽  
Materials Science ◽  
Classical Mechanics ◽  
Least Action ◽  
Principle Of Least Action ◽  
Theory Of Gravitation ◽  
Mathematical Equations ◽  
Deep Significance

How the Principle of Least Action underlies all physics (all physics that can be reduced to mathematical equations) is explained at a qualitative, semi-popular level. It even applies to smartphones. The domains of classical mechanics, continuum mechanics, materials science, light and electromagnetic waves, special and general relativity (Einstein’s Theory of Gravitation), electrodynamics, quantumelectrodynamics (QED), hydrodynamics, physical chemistry, statistical mechanics, and the quantum world, are examined. It is shown that the Principles of Least Time, Least Resistance, and Maximal Ageing, and Lenz’s Law are, in fact, examples of the Principle of Least Action. It is also shown how Planck’s constant is a measure of “absolute smallness,” and its units are the units of action. Never again, post quantum mechanics, can there be any doubt about the deep significance of action in physics.

A Principle in classical mechanics with a ‘relativistic’ path-element extending the principle of least action

1955 ◽  
Vol 51 (3) ◽  
pp. 469-475
Author(s):  
Edgar B. Schieldrop
Keyword(s):  
Kinetic Energy ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Sufficient Condition ◽  
Least Action ◽  
Actual Motion ◽  
Principle Of Least Action ◽  
Terminal Values ◽  
Newtonian Space ◽  
Image Position

1. A particle with mass m and coordinates x1x2, x3 relative to a set of rectangular axes fixed in Newtonian space is moving in a field of conservative forces with a potential energy V(x1, x2, x3) and a kinetic energyThe equations of motion, written(representing the three equations i = l, i = 2, i = 3 in a way to be used in this paper), constitute, as they stand, a sufficient condition in order to ensurein the sense that the Hamiltonian integral has a stationary value if the actual motion is compared with neighbouring motions with the same terminal positions and the same terminal values of the time as in the actual motion.

scholarly journals Reply to the Comments on: Tian Zhao et al. The Principle of Least Action for Reversible Thermodynamic Processes and Cycles. Entropy 2018, 20, 542

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 986
Author(s):  
Zeng-Yuan Guo ◽  
Tian Zhao ◽  
Yu-Chao Hua
Keyword(s):  
Least Action ◽  
Principle Of Least Action ◽  
Thermodynamic Processes

The purpose of this reply is to provide a discussion and closure for the comment paper by Dr. Bormashenko on the present authors’ article, which discussed the application of the principle of least action in reversible thermodynamic processes and cycles. Dr. Bormashenko’s questions and misunderstandings are responded to, and the differences between the present authors’ work and Lucia’s are also presented.

scholarly journals Indeterminism in quantum mechanics: beyond and/or within causation

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Energy Conservation ◽  
Mathematical Problem ◽  
Classical Mechanics ◽  
Axiom Of Choice ◽  
Classical Physics ◽  
Least Action ◽  
Matrix Mechanics ◽  
Principle Of Least Action ◽  
The Axiom Of Choice

The problem of indeterminism in quantum mechanics usually being considered as a generalization determinism of classical mechanics and physics for the case of discrete (quantum) changes is interpreted as an only mathematical problem referring to the relation of a set of independent choices to a well-ordered series therefore regulated by the equivalence of the axiom of choice and the well-ordering “theorem”. The former corresponds to quantum indeterminism, and the latter, to classical determinism. No other premises (besides the above only mathematical equivalence) are necessary to explain how the probabilistic causation of quantum mechanics refers to the unambiguous determinism of classical physics. The same equivalence underlies the mathematical formalism of quantum mechanics. It merged the well-ordered components of the vectors of Heisenberg’s matrix mechanics and the non-ordered members of the wave functions of Schrödinger’s undulatory mechanics. The mathematical condition of that merging is just the equivalence of the axiom of choice and the well-ordering theorem implying in turn Max Born’s probabilistic interpretation of quantum mechanics. Particularly, energy conservation is justified differently than classical physics. It is due to the equivalence at issue rather than to the principle of least action. One may involve two forms of energy conservation corresponding whether to the smooth changes of classical physics or to the discrete changes of quantum mechanics. Further both kinds of changes can be equated to each other under the unified energy conservation as well as the conditions for the violation of energy conservation to be investigated therefore directing to a certain generalization of energy conservation.

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