# A Quasi-Statistical Approach to the Boltzmann Entropy Equation Based on a Novel Energy Conservation Principle

## Authors

• Saeed Shahsavari Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran
• Mehran Moradi Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran
• Pooya Torkaman School of Metallurgy and Material Engineering, Iran University of Science and Technology, Tehran, Iran

## Keywords:

Energy space, energy conservation principle, entropy, energy structure, statistical mechanics, Boltzmann entropy equation

## Abstract

Boltzmann entropy equation is gained according to the statistical mechanics directly and general dependence between entropy and probability is obtained. Based on the second law of thermodynamics with a glance at the Boltzmann entropy equation, it can be deduced that physical processes are done in a direction that the probability of the system and total entropy increase. In fact, the possible process performing states and their entropy variations will be determined at a specific energy level. In this paper, an entropy equation is gained by using a new quasi-statistical approach to the physical processes as well as a novel energy conservation principle. The variation of the "energy structure equation”, as an equation to formulate the performed process using activated energy components of the system and their dependence, is studied in different possible paths by using the energy conservation principle directly. Despite the classical mechanics that all particles are studied, in the novel approach, "particular processes" as all processes that have the same active independent energy components are studied at "various conditions"; in other words, all conditions that same energy amount is applied to the system. One of the advantages of this novel approach is that the volume of the needed calculations will be decreased mainly in comparison with the Boltzmann entropy equation. Dependence of the entropy and rate of the energy components is gained from the novel energy conservation principle. The gained relation, expressed by energy components of the system, is considered with no constraints on the structure of the system but has a common basis with the Boltzmann entropy equation. In fact, by using a novel macroscopic-statistical approach, the entropy variation of a physical system is studied.

## Author Biographies

### Saeed Shahsavari, Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran

s.shahsavari@me.iut.ac.ir

### Pooya Torkaman, School of Metallurgy and Material Engineering, Iran University of Science and Technology, Tehran, Iran

Pooya_torkaman@metaleng.iust.ac.ir

2023-01-30

## How to Cite

Saeed Shahsavari, Mehran Moradi, & Pooya Torkaman. (2023). A Quasi-Statistical Approach to the Boltzmann Entropy Equation Based on a Novel Energy Conservation Principle. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 101(2), 99–110. https://doi.org/10.37934/arfmts.101.2.99110

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