The problem of engines in statistical physics

Abstract

Engines are open systems that can generate work cyclically, at the expense of an external disequilibrium. They are ubiquitous in nature and technology, but the course of mathematical physics over the last 300 years has tended to make their dynamics in time a theoretical blind spot. This has hampered the usefulness of statistical mechanics applied to active systems, including living matter. We argue that recent advances in the theory of open quantum systems, coupled with renewed interest in understanding how active forces result from positive feedback between different macroscopic degrees of freedom in the presence of dissipation, point to a more realistic description of autonomous engines. We propose a general conceptualization of an engine that helps clarify the distinction between its heat and work outputs. Based on this, we show how the external loading force and the thermal noise may be incorporated into the relevant equations of motion. This modifies the usual Fokker-Planck and Langevin equations, offering a thermodynamically complete formulation of the irreversible dynamics of simple oscillating and rotating engines.

25 pages, 7 figures

References in corpus (7)

• Artificial Brownian motors: Controlling transport on the nanoscale
• Thermodynamic uncertainty relation for biomolecular processes
• Scattering theory of current-induced forces in mesoscopic systems
• Current-induced forces: a simple derivation
• Continuity and boundary conditions in thermodynamics: From Carnot's efficiency to efficiencies at maximum power
• Stochastic thermodynamics of self-oscillations: the electron shuttle
• From the GKLS equation to the theory of solar and fuel cells