Abstract
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.
Highlights
The principle of least action is a fundamental physics principle that is widely applied in physics [1].In optics, Fermat proposed Fermat’s principle, which states that the path taken between two points by a ray of light is the path that can be traversed in the least time [2], such as a straight ray in a uniform medium, or the refraction of light passing through an interface between two media.In this principle, the traversal time is the optimization object and the product of the refraction index and the optical path is regarded as the action
Hamilton proposed Hamilton’s principle in 1834, a general principle of least action for classical mechanics, which states that the dynamics of a physical system are determined by a variational problem for a functional based on its Lagrangian, which contains all the physical information concerning the system and the forces acting on it [4,5]
For artificial optimization problems, minimizing its action based on the known fundamental law and governing relationship leads to its optimal path, which corresponds to its optimization object
Summary
The principle of least action is a fundamental physics principle that is widely applied in physics [1]. Dharma-Wardana indicated that mechanical motion in nature already incorporates the principle of the least expensive route [12], which yields the notion that natural phenomena represent optimized processes In this view, natural problems without manual intervention may be regarded as a category of optimization problems, with the action playing the role of the optimization criterion. That is why entransy dissipation, rather than entropy generation, is the optimization criterion of heat transfer without heat–work conversion For both reversible thermodynamic processes and cycles, it seems that the concept of action and the principle of least action are seldom discussed in the literature. This study analyzes a class of general reversible thermodynamic processes and cycles to develop their principle of least action, which may lead to the optimization of thermodynamic cycles
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