Fig. 2: Buildup of irreversibility in the non-Gaussian Stirling engine at finite τ.

In a and b, we show probability distribution of work done per cycle ρ(W_cyc) for the Gaussian engine and for the non-Gaussian engine with κ = 20 in the hot reservoir, respectively, for different cycle durations. τ = 18.8 s (blue triangles), τ = 10.6 s (red circles), and τ = 5.6 s (black squares). Solid lines represent corresponding Gaussian fits to the data. c Red hollow and solid squares show the average work done per cycle 〈W_cyc〉 and the most-probable work W^*, respectively, for the non-Gaussian engine with κ = 20 for the hot reservoir at various τ. The red solid line is a fit to Eq. (1). Black hollow and solid circles show 〈W_cyc〉 and W^* respectively for the thermal/Gaussian engine. At large τ, the experimentally calculated work for these engines agrees with theoretically calculated quasistatic work W_∞ indicated by the small red horizontal line for the non-Gaussian engine with κ = 20 for the hot reservoir and by the black line for the Gaussian engine. Mean work 〈W_cyc〉 is calculated for each realization of the engine over 450 cycles for τ = 3.7 s, 400 cycles for τ = 4 s, 278 cycles for τ = 5.6 s, 193 cycles for τ = 8 s, 150 cycles for τ = 10.6 s, 85 cycles for τ = 18.8 s and 50 cycles for τ = 32 s. d The ratio \(k\langle {x}^{2}\rangle /{k}_{{{{{{{{\rm{B}}}}}}}}}{T}_{{{{{{{{\rm{eff}}}}}}}}}^{{{{{{{{\rm{H}}}}}}}}}\) calculated at the midpoint of the hot isotherm for various τ is showed by the red squares for the non-Gaussian engine with κ = 20 in the hot reservoir and by the black circles for the Gaussian engine. The horizontal line indicates the equilibrium condition, which is violated inside the shaded gray region, in the case of the non-Gaussian engine with κ = 20 in the hot reservoir. The error bars indicate the standard deviations of the mean and the most probable quantities across different experiments.