Time-dependent thermodynamic relationships for a Brownian particle that walks in a complex network

The thermodynamics feature of systems that are driven out of equilibrium is explored for M Brownian ratchets that are arranged in a complex network. The exact time-dependent solution depicts that as the network size increases, the entropy S, entropy production ep(t), and entropy extraction hd(t) of the system step up which is feasible since these thermodynamic quantities exhibit an extensive property. In other words, as the number of lattice size increases, the entropy S, entropy production ep(t), and entropy extraction hd(t) step up revealing that these complex networks can not be reduced into the corresponding one-dimensional lattice. On the contrary, the rate for thermodynamic relations such as the velocity V, entropy production rate[e] p(t) and entropy extraction rate [Formula] become independent of the network size in the long time limit. The exact analytic result also shows that the free energy decreases with the system size. The model system is further analyzed by including heat transfer via kinetic energy. Since the heat exchange via kinetic energy does not affect the energy extraction rate, the heat dumped to the cold reservoirs contributes only to the internal entropy production. As the result, such systems exhibit a higher degree of irreversibility. The thermodynamic features of a system that operates between hot and cold baths are also compared and contrasted with a system that operates in a heat bath where its temperature varies linearly along the reaction coordinate. Regardless of the network arrangements, the entropy, entropy production, and extraction rates are considerably larger for the linearly varying temperature case than a system that operates between hot and cold baths. PACS numbersValid PACS appear here