Adiabatic processes like isothermal processes

The objective of this work is to show that adiabatic processes can be very similar to isothermal ones. First, we show that the criteria for the compatibility of linear-response theory with the second law of thermodynamics for thermally isolated systems are the same as those for systems performing isothermal processes. Motivated by such a result, we explore the thermodynamic consequences of the time-average excess work, observing an unexpected existence of a well-defined relaxation time for thermally isolated systems that obeys the second law of thermodynamics. This is justified by recognizing that such systems, in the usual sense, present random relaxation time, which can be averaged by taking the time average of the relaxation function. Such a proceeding is very similar to what happens in isothermal processes, where a stochastic average must be done on the relaxation function to have a well-defined relaxation time. In the end, we analyze the Landau-Zener model from this new point of view, discussing the construction of slowly-varying processes from linear-response theory and observing negative entropy production rates for nonmonotonic and rapid protocols.

Automated summary

The objective of this work is to demonstrate the similarities between adiabatic and isothermal processes. By examining the criteria for the compatibility of linear-response theory with the second law of thermodynamics in thermally isolated systems, we find that they are the same as those for isothermal processes. This leads us to explore the thermodynamic consequences of time-average excess work, demonstrating the existence of a well-defined relaxation time obeying the second law of thermodynamics in thermally isolated systems. We apply this understanding to the Landau-Zener model, observing negative entropy production rates for nonmonotonic and rapid protocols.