Laboratoire Matière et Systèmes Complexes

Maximum efficiency of heat engines revisited

Naoto Shiraishi

Abstract: In this talk, we focus on two important classes of heat engines and investigate their maximum efficiency. We especially focus on the attainability for the Carnot efficiency (CE).

In the first part, we consider finite power heat engines. Although it is well known that the quasistatic limit leads to the CE, its converse has still been an open problem. Conventional thermodynamics does not prohibit finite power engines with the CE. Moreover, with broken time-reversal symmetry (such as a system with a magnetic field) linear irreversible thermodynamics neither prohibits such engines even in linear response regime [1]. Triggered by this, many specific models with broken time-reversal symmetry have been studied, but it has turned out that all of them in fact never attain the CE with finite power [2-4]. Therefore, one anticipates the general no-go theorem which prohibits finite power heat engines to attain the CE even with broken time-reversal symmetry and even beyond the linear response regime. In this talk, by using the method of partial entropy production [5], we prove the general no-go theorem for Markovian systems [6]. In addition, we derive a general trade-off relation between efficiency and power.

In the second part, we consider autonomous heat engines. Here, the word autonomous stands for systems with no time-dependent control parameter in non-equilibrium steady states. A prominent example of autonomous heat engines is Feynman’s ratchet, which converts heat flux into work automatically. Opposed to Feynman’s anticipation [7], it has been revealed that the ratchet never attains the CE even in the quasistatic limit [8, 9]. Another example is the autonomous Maxwell’s demon [5,10], which performs measurement and feedback processes automatically and attains the CE in contrast to Feynman’s ratchet. On the basis of these studies on specific models, we clarify the general necessary condition for autonomous heat engines to attain the CE, which is a certain type of singularity [11].

References [1] G. Benenti, K. Saito, and G. Casati, Phys. Rev. Lett. 106, 230602 (2011). [2] K. Brandner, K. Saito, and U. Seifert, Phys. Rev. Lett. 110, 070603 (2013). [3] V. Balachandran, G. Beneti, and G. Casati, Phys. Rev. B 87, 165419 (2013). [4] K. Proesmans and C. Van den Broeck, Phys. Rev. Lett. 115, 090601 (2015). [5] N. Shiraishi and T. Sagawa, Phys. Rev. E 91, 012130 (2015). [6] N. Shiraishi and K. Saito, in preparation [7] R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Volume I. Addison Wesley (1963). [8] J. M. R. Parrondo and P. Espanol, Am. J. Phys. 64, 1125 (1996). [9] T. Hondou and K. Sekimoto, Phys. Rev. E 62, 6021 (2000). [10] K. Sekimoto, Physica D 205, 242 (2005). [11] N. Shiraishi, Phys. Rev. E 92, 050101 (2015).

Vendredi 12 Fevrier à 12h30 en salle 646A