Suppose that we model the entire universe (i.e. the entirety of the known physical universe) as a huge isolated system, using molecular dynamics (MD for short).
The question is: How would you show that the entropy of such a system does in fact always increase? that it neither decreases nor stays the same?
Traditionally dynamic analysis is done using Newtonโs universal laws of the equation of motion. According to the laws of Newtonian mechanics, the x, y, z, space-time coordinate system does not include a term for energy loss, an empirical damping term โCโ is used in the dynamic equilibrium equation. Energy loss in any system is governed by the laws of thermodynamics. Unified Mechanics Theory (UMT) unifies the universal laws of motion of Newton and the laws of thermodynamics at ab-initio level.
The unified mechanics theory (UMT) is ab-initio unification of the second law of thermodynamics and Newton's universal laws of motion, in which Boltzmann's second law of entropy formulation governs dissipation & degradation. Hence, the unified mechanics theory does not require any empirical dissipation & degradation potential function or an empirical void evolution function. Material degradation is quantified on the Thermodynamic state index (TSI) axis based on the specific entropy production, which starts at zero and asymptotically approaches one at failure.
The unified mechanics theory (UMT) was used to develop a model to predict the fatigue life of pre-corroded steel samples with BCC structure. Details of the experimental validation are also provided.
If you are interested in the most recent advances in physics-based Fatigue, Fracture, Failure Prediction, and Structural Health Monitoring
You may find this publication helpful.
free download site https://www.mdpi.com/books/pdfview/book/3299
If you ever wanted to attend a conference where Natural Sciences meet Social Sciences. You may want to consider attending,
In the study of thermoelastic actuation of dielectric elastomer, we can write the Helmholtz free-energy as a function of stretch ratio, nominal electric displacement and temperature (T).
The entropy (S) is the negative partial differential coefficient of W with respect of temperature (T). And we can see the change of S is due to three components: deformation, heat conduction and polarization. In an isothermal state, the deformation part has been fully investigated by Arruda and Boyce in 1993, but the polarization-induced entropy (Sp) has not been clearly stated.
The following PowerPoint file is from the talk which I gave in my research group recently. It is also my understanding and reading notes from a serial of papers by Prof. Udo Seifert, in which he generalized the entropy production on a single trajectory of the small system such as a molecular machine. It mainly addresses three questions:
