We use the Shannon (information) entropy to define an “entropic” temperature for 1D nonequilibrium system with heat flux. In contrast to the kinetic temperature, which is related to the average kinetic energy, the nonequilibrium entropic temperature is related to the changes in entropy and serves as a criterion for thermalization. However, the direction and value of the heat flux is controlled by the gradient of the kinetic temperature, whereas space-time evolution and the space-time evolution of the heat flux are governed by the hyperbolic heat conduction equation. The extended nonequilibrium variables, namely, entropy, entropic temperature, thermal conductivity, and heat capacity demonstrate a third-law-like behavior at high deviation from equilibrium when the heat flux tends to its maximum value, even at nonzero value of the kinetic temperature. The ratio of the heat flux to its maximum possible value plays a role of an order parameter – it varies from zero in the equilibrium (disordered) state to unity in the nonequilibrium (ordered) state.
Thermodynamic performance analysis of microscopic Feynman’s engine has always been a hot topic, since it can reveal the operating mechanism of the system and give out the suggestions of performance improvement. The present work explores the optimal performance regions of the ratchet operating, respectively, as heat engine and refrigerator. The major purpose is to obtain the optimal performance bunds and provide theoretical guidelines for the designs of practical microscopic ratchet engine systems. Based on an irreversible Feynman’s ratchet engine, the optimal power output versus thermal efficiency performance and the optimal cooling load versus COP performance in different operation modes are analyzed. The effects of irreversible heat leakage and major design parameters are also explored. By further introducing the ecological function, efficient power, and figure of merit criteria, performance characteristics of ratchet device with different optimization indexes are analyzed and compared with each other. The optimal performance regions concerning different optimization criteria are obtained. The results show that by reasonably selecting design parameters, Feynman’s ratchet can attain the optimal operation conditions for different design purposes.