Linear and nonlinear 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 τ : their relative excursions, δ and 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 δ and the fluxes are linear in the forces through a τ -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 τ → ∞ and the the small force limit δ, → 0 are not directly related.

Anomalous Brownian refrigerator

“…Detailed theoretical treatment of Carnottype micro heat engine, involving both quasistatic and non-quasistatic (i.e., finite cycle time) features, have also been documented [33,34,35,36,37,38]. These features reveal the fundamental differences between micro and macro heat engines due to thermal fluctuations, reflected in the distributions of various thermodynamic quantities (e.g., work, heat exchange, efficiency etc.).…”

“…Heat engines and refrigerators at nano-scale is a subject of current study [29,30,31,32,33,34,35,36,37]. Detailed theoretical treatment of Carnottype micro heat engine, involving both quasistatic and non-quasistatic (i.e., finite cycle time) features, have also been documented [33,34,35,36,37,38].…”

Operational characteristics of single-particle heat engines and refrigerators with time-asymmetric protocol

“…Phase diagram shows several interesting features, often counterintuitive. The distribution of stochastic efficiency and COP is broad and exhibits power law tails.In recent years a lot of interest has been generated in the study of stochastic single particle heat engines and refrigerators [1,2,3,4,5,6,7,8,9,10,11]. Engines at nanoscale are ubiquitous in biology [12,13,14] and become increasingly pertinent synthetically.…”

Thermodynamics of slow solutions to the gas-piston equations

“…As it emerges by Figure 3, R ≈ 1 for various value of N and ε, so , we reasonably say that x num (s) is attracted by eq. (16). This means that the dynamical equilibrium solution has a quite general usefulness.…”

“…Another problem which is conceptually simple, but difficult to treat is the non-equilibrium thermodynamics of a perfect gas enclosed by a cylindrical canister with a movable piston and in contact with a heat reservoir (see Figure 1). For this system there are multiple valid approaches: for example the one particle gas approach [7] and its legacy [8][9][10][11], the explicit-friction formulae approach [12][13][14], and the gas particles-average approach [15][16][17][18]. Among those references [15] is particularly interesting: there, the authors assumed that (i) the gas is perfect and 1-dimensional; (ii) the piston and each gas particle undergoes elastic collisions, so work is the energy exchanged in this way; (iii) the velocity of a gas particle is randomly changed according to the Maxwell-Boltzmann distribution of the reservoir when reservoir-gas particle collisions occurs [19] and heat is the change in energy of the gas; (iv) the gas distribution is always Maxwellian although gas-reservoir and gas-piston collisions change the temperature of the gas over time.…”