Thermodynamic length, geometric efficiency and Legendre invariance

Thermodynamic length is a metric distance between equilibrium thermodynamic states that asymptotically bounds the dissipation induced by finite time transformation of system. By means length, we first evaluate departures from ideal to real gases in geometric thermodynamics with and without Legendre invariance. In particular, investigate Ruppeiner geometrothermodynamic formalisms. Afterwards, formulate strategy relate lengths efficiency systems both aforementioned frameworks working assumption small deviations ideality. this respect, propose definition built up analogy quantum systems. We show result higher for fluids. Moreover, stress could be used as novel way distinguish non-ideal thermal behaviors. such way, it useful quantify ideality variety gases. Finally, discuss corresponding applications our recipe classical systems, noticing findings help geometrically grasping nature different metrizations on manifolds states.