Adiabatic processes like isothermal processes

TL;DR

This paper demonstrates that adiabatic processes can exhibit thermodynamic behaviors similar to isothermal ones, revealing new insights into relaxation times and entropy production through linear-response theory and the Landau-Zener model.

Contribution

It shows the compatibility of linear-response theory with the Second Law for adiabatic processes and introduces the concept of a well-defined relaxation time in thermally isolated systems.

Findings

Existence of a well-defined relaxation time in isolated systems

Negative entropy production rates in certain protocols

Similarity between adiabatic and isothermal relaxation behaviors

Abstract

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 procedure 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 non-monotonic and rapid protocols.