The geometry of Gibbs fundamental relation in non-equilibrium thermodynamics E.M. Knobbe a , D.J.E.M. Roekaerts a a Department of Multi-Scale Physics, Delft University of Technology, Delft, The Netherlands Summary This contribution presents an outline of a new mathematical formulation for non-equilibrium thermodynamics based on contact geometry. A non-equilibrium state space is introduced as third key element besides both laws of thermodynamics. A generalization of the Gibbs fundamental relation is than obtained by identifying some of the canonical coordinates of this state space. Finally, it will be shown how the physical phenomena of chemical reactions and phase changes fit within the proposed mathematical framework. Keywords: Contact geometry, non-equilibrium thermodynamics, Gibbs fundamental relation 1. Introduction In his monumental work “On the Equilibrium of Heterogeneous Substances” Josiah Willard Gibbs [2] postulates a relation that is fundamental for thermodynamics, viz. dU = T dS - p dV + nspc X α=1 μ α dm α . Gibbs postulated this relation for a mixture of n spc non-reacting, chemical species in a closed system that is in equilibrium. The major aim of the work presented in this contribution is to introduce a mathematical formulation that extends the above relation to non-equilibrium thermodynamics. An essential criterion for the derivation of this mathematical formulation is that it is not based on the Local equilibrium hypothesis. Many approaches derive a generalization of the Gibbs fundamental relation from the First and Second law of thermodynamics, which are then formulated as Master balance laws. Such an approach obscures the meaning of the differential d in the above equation, therefore a different approach will be presented in this contribution [5]. Furthermore, opposite to for instance Extended Irreversible Thermodynamics [4], is in this approach a diffusive flux not a thermodynamic state variable. 2. Contact geometry 2.1 Non-equilibrium thermodynamic state space This extended abstract presents only an outline of the complete mathematical framework [5] and starts with a brief recapitulation of the familiar thermodynamic concepts. A thermodynamic state function is the 0-form M that is generated by the exact 1-form μ 1 , viz. μ 1 = dM with dμ 1 =0 such that I dM =0. Corresponding author is E.M. Knobbe E. Knobbe : E-mail: e.knobbe@de.tecosim.com, WWW: http://www.msp.tudelft.nl D. Roekaerts : E-mail: D.J.E.M.Roekaerts@TUDelft.nl, Telephone: +31 (0)15 278 24 70