Fast-forward approach to stochastic heat engine

Fokker-Planck equation on metric graphs

“…It describes the time evolution of the probability density function of the velocity of a particle under the influence of drag forces and random forces. Since from its discovering in 1914, the Fokker-Planck equation found numerous applications in plasma physics [16,17], particle and beam physics [12],thermodynamics [15,38], condensed matter [10], real gases [14,19], fluid dynamics [25], neural networks [36,37,[40][41][42], traffic modelling [27][28][29] and even in socio-and econo-physics [30][31][32][33][34]. Different aspects of mathematical properties [22] of the Fokker-Planck equation (FPE) have been widely studied and various schemes have been proposed [35] for its numerical solution.…”

A microscopic theory of Curzon-Ahlborn heat engine

“…Nevertheless, the symmetric low-dissipation regime seems to be irrelevant to the endoreversible assumption [4][5][6][7][13][14][15], even though both lead to the CA efficiency as the EMP. In some other dynamical models, the EMP deviates from the CA efficiency [11,[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], probably due to different situations of these models. Thus, a thorough understanding about the preconditions under which the CA efficiency is the EMP remains to be clarified.…”

Geodesic path for the minimal energy cost in shortcuts to isothermality

“…Shortcut to isothermality was proposed as a finitetime driving strategy to steer the system evolving along the path of instantaneous equilibrium states [9]. The strategy has been applied in reducing transition time between equilibrium states [10][11][12], improving the efficiency of free-energy estimation [13], constructing finitetime heat engines [14][15][16], and controlling biological evolutions [4,5]. The cost of the finite-time operation is the additional energy cost due to irreversibility posted by the fundamental thermodynamic law.…”