Thermodynamics of driven systems

A geometrical formulation of thermodynamics is carried in this paper to a domain that includes dynamics and driven systems. Let it be known from experience that the behavior of an externally unforced or a driven system is well described in a state space N. The thermodynamics of the system is a geometrical structure in N that arises from an analysis of the time evolution in a more microscopic (i.e., depicting more details) state space M. If in particular the system is externally unforced then the state space N can be chosen to be the state space ${\mathit{N}}_{\mathrm{ET}}$ of equilibrium thermodynamics. The geometrical structure in ${\mathit{N}}_{\mathrm{ET}}$, obtained by analyzing the time evolution in a more microscopic state space M, appears to be the geometrical formulation of classical equilibrium thermodynamics. The general formulation of thermodynamics introduced in this paper is illustrated by the example of a k-component system undergoing a chemical reaction.