Thermodynamic length, geometric efficiency and Legendre invariance
Cafaro C. Luongo O. Mancini S. Quevedo H.
15 March 2022Elsevier B.V.
Physica A: Statistical Mechanics and its Applications
2022#590
Thermodynamic length is a metric distance between equilibrium thermodynamic states that asymptotically bounds the dissipation induced by a finite time transformation of a thermodynamic system. By means of thermodynamic length, we first evaluate the departures from ideal to real gases in geometric thermodynamics with and without Legendre invariance. In particular, we investigate ideal and real gases in the Ruppeiner and geometrothermodynamic formalisms. Afterwards, we formulate a strategy to relate thermodynamic lengths to efficiency of thermodynamic systems in both the aforementioned frameworks in the working assumption of small deviations from ideality. In this respect, we propose a geometric efficiency definition built up in analogy to quantum thermodynamic systems. We show the result that this efficiency is higher for geometrothermodynamic fluids. Moreover, we stress this efficiency could be used as a novel geometric way to distinguish ideal from non-ideal thermal behaviors. In such a way, it could be useful to quantify deviations from ideality for a variety of real gases. Finally, we discuss the corresponding applications of our recipe to classical thermodynamic systems, noticing that our findings could help geometrically grasping the nature of different metrizations on manifolds of equilibrium thermal states.
Differential geometry , Fundamental problems and formalism of general relativity , General relativity , Thermodynamics
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SUNY Polytechnic Institute, 257 Fuller Road, Albany, 12203, NY, United States
Scuola di Scienze e Tecnologie, Università di Camerino, Via Madonna delle Carceri 9, Camerino, 62032, Italy
Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, Pisa, 56127, Italy
NNLOT, Al-Farabi Kazakh National University, Al-Farabi av. 71, Almaty, 050040, Kazakhstan
Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Via Alessandro Pascoli 23c, Perugia, 06123, Italy
Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de México, Mexico, D.F. 04510, Mexico
Dipartimento di Fisica and Icra, Universita di Roma “La Sapienza”, Piazzale Aldo Moro 5, Roma, I-00185, Italy
Institute for Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
SUNY Polytechnic Institute
Scuola di Scienze e Tecnologie
Dipartimento di Matematica
NNLOT
Istituto Nazionale di Fisica Nucleare
Instituto de Ciencias Nucleares
Dipartimento di Fisica and Icra
Institute for Experimental and Theoretical Physics
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