Time–energy uncertainty principle for irreversible heat engines

Abstract

<jats:p>Even though irreversibility is one of the major hallmarks of any real-life process, an actual understanding of irreversible processes remains still mostly semi-empirical. In this paper, we formulate a thermodynamic uncertainty principle for irreversible heat engines operating with an ideal gas as a working medium. In particular, we show that the time needed to run through such an irreversible cycle multiplied by the irreversible work lost in the cycle is bounded from below by an irreducible and process-dependent constant that has the dimension of an action. The constant in question depends on a typical scale of the process and becomes comparable to Planck’s constant at the length scale of the order Bohr radius, i.e. the scale that corresponds to the smallest distance on which the ideal gas paradigm realistically applies.</jats:p> <jats:p>This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.</jats:p>

Nonequilibrium thermodynamics: emergent and fundamental

“…The third benchmark, backward compatibility, should precede the mathematical structure. The compatibility with a statistical treatment, based on a given microscopic or mesoscopic material composition, is a clear benchmark of any general phenomenology and appears here in the papers [1,10,12]. In particular, the compatibility with the kinetic theory is important in [3,[6][7][8].…”

“…For example, for discrete systems, that is homogeneous or point-like material models, the space-time aspects are less important. These systems are treated in [1,10,11] and also partially in [3,5]. Quantum systems are discrete, too [1,11].…”