Linear and non-linear thermodynamics of a kinetic heat engine with fast transformations

Abstract

We investigate a kinetic heat engine model constituted by particles enclosed in a box where one side acts as a thermostat and the opposite side is a piston exerting a given pressure. Pressure and temperature are varied in a cyclical protocol of period $\tau$ : their relative excursions, $\delta$ and $\epsilon$ respectively, constitute the thermodynamic forces dragging the system out-of-equilibrium. The analysis of the entropy production of the system allows to define the conjugated fluxes, which are proportional to the extracted work and the consumed heat. In the limit of small $\delta$ and $\epsilon$ the fluxes are linear in the forces through a $\tau$-dependent Onsager matrix whose off-diagonal elements satisfy a reciprocal relation. The dynamics of the piston can be approximated, through a coarse-graining procedure, by a Klein-Kramers equation which - in the linear regime - yields analytic expressions for the Onsager coefficients and the entropy production. A study of the efficiency at maximum power shows that the Curzon-Ahlborn formula is always an upper limit which is approached at increasing values of the thermodynamic forces, i.e. outside of the linear regime. In all our analysis the adiabatic limit $\tau \to \infty$ and the the small force limit $\delta ,\epsilon \to 0$ are not directly related.

arXiv comment10 pages, 9 figures

References in corpus (24)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Efficiency at maximum power: An analytically solvable model for stochastic heat engines
• Efficiency at maximum power of low dissipation Carnot engines
• Universality of efficiency at maximum power
• The unlikely Carnot efficiency
• Comparison of far-from-equilibrium work relations
• Thermodynamics of Micro- and Nano-Systems Driven by Periodic Temperature Variations
• Efficiency statistics at all times: Carnot limit at finite power
• Anomalous thermodynamics at the micro-scale
• Onsager coefficients of a finite-time Carnot cycle
• Onsager coefficients in periodically driven systems
• Irreversible effects of memory
• Molecular kinetic analysis of a finite-time Carnot cycle
• Hamiltonian dynamics, nanosystems, and nonequilibrium statistical mechanics
• Estimate of temperature and its uncertainty in small systems
• Efficiency of Single Particle Engines
• Jarzynski Equality, Crooks Fluctuation Theorem and the Fluctuation Theorems of Heat for Arbitrary Initial States
• Macroscopic equations for the adiabatic piston
• Nonequilibrium Statistical Mechanics for Adiabatic Piston Problem
• A kinetic model for the finite-time thermodynamics of small heat engines
• Fluctuations in partitioning systems with few degrees of freedom

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• Hierarchical Onsager symmetries in adiabatically driven linear irreversible heat engines
• General linear thermodynamics for periodically driven systems with multiple reservoirs
• Thermodynamic optimization of an electric circuit as a non-steady energy converter
• Molecular kinetic analysis of a local equilibrium Carnot cycle
• Quasi-linear irreversible thermodynamics of a low-temperature-differential kinematic Stirling heat engine
• Entropy Anomaly in Langevin-Kramers Dynamics with a Temperature Gradient, Matrix Drag, and Magnetic Field
• Thermodynamics of slow solutions to the Gas-Piston equations