Adiabatic processes like isothermal processes

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.

9 pages, 5 figures

References in corpus (6)

• Exploring local quantum many-body relaxation by atoms in optical superlattices
• Optimal driving of isothermal processes close to equilibrium
• Degenerate optimal paths in thermally isolated systems
• Fluctuation relations and strong inequalities for thermally isolated systems
• Failure of the geometric approach prediction of excess work scaling for open and isolated quantum systems
• Fluctuation theorem for irreversible entropy production in electrical conduction

Cited by in corpus (6)

• Analytical solution for optimal protocols of weak drivings
• Quantum Ising chain with time-averaged work in linear response theory
• Fluctuation theorem for time-averaged work
• Casimir-Onsager matrix for weakly driven processes
• Analytical shortcuts to adiabaticity of weakly driven processes
• Unifying Kibble-Zurek Mechanism in Weakly Driven Processes