Preprint Article Version 1 This version is not peer-reviewed

Finding Exact Forms on a Thermodynamic Manifold

Version 1 : Received: 9 October 2018 / Approved: 10 October 2018 / Online: 10 October 2018 (05:19:04 CEST)

How to cite: Ju, C.; Stalzer, M. Finding Exact Forms on a Thermodynamic Manifold. Preprints 2018, 2018100202 (doi: 10.20944/preprints201810.0202.v1). Ju, C.; Stalzer, M. Finding Exact Forms on a Thermodynamic Manifold. Preprints 2018, 2018100202 (doi: 10.20944/preprints201810.0202.v1).

Abstract

Because only two variables are needed to characterize a simple thermodynamic system in equilibrium, any such system is constrained on a 2D manifold. Of particular interest are the exact 1-forms on the cotangent space of that manifold, since the integral of exact 1-forms is path-independent, a crucial property satisfied by state variables such as internal energy dE and entropy dS. Our prior work [1] shows that given an appropriate language of vector calculus, a machine can re-discover the Maxwell equations and the incompressible Navier-Stokes equations from data. In this paper, We enhance this language by including differential forms and show that machines can re-discover the equation for entropy dS given data. Since entropy appears in various fields of science in different guises, a potential extension of this work is to use the machinery developed in this paper to let machines discover the expressions for entropy from data in fields other than classical thermodynamics.

Subject Areas

thermodynamics; entropy; artificial intelligence; differential geometry; computational physics

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