Fluctuation relations and strong inequalities for thermally isolated systems

For processes during which a macroscopic system exchanges no heat with its surroundings, the second law of thermodynamics places two lower bounds on the amount of work performed on the system: a weak bound, expressed in terms of a fixed-temperature free energy difference, W >= Delta F-T, and a strong bound, given by a fixed-entropy internal energy difference, W >= Delta E-S. It is known that statistical inequalities related to the weak bound can be obtained from the nonequilibrium work relation, < e(-beta W)> = e(-beta Delta FT). Here we derive an integral fluctuation relation < e(-beta x)> = 1 that is constructed specifically for adiabatic processes, and we use this result to obtain inequalities related to the strong bound, W >= Delta E-S. We provide both classical and quantum derivations of these results. (C) 2019 Elsevier B.V. All rights reserved.