Fluctuation relations and strong inequalities for thermally isolated systems

Abstract

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, $W\ge \Delta F_T$ , and a strong bound, given by a fixed-entropy internal energy difference, $W\ge \Delta E_S$ . It is known that statistical inequalities related to the weak bound can be obtained from the nonequilibrium work relation, $⟨\exp (-\beta W)⟩=\exp (-\beta \Delta F_T)$ . Here we derive an integral fluctuation relation $⟨\exp (-\beta X)⟩=1$ that is constructed specifically for adiabatic processes, and we use this result to obtain inequalities related to the strong bound, $W\ge \Delta E_S$ . We provide both classical and quantum derivations of these results.

Dedicated to the memory of Christian Van den Broeck

References in corpus (13)

• Fluctuation theorems: Work is not an observable
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• Gibbs, Boltzmann, and negative temperatures
• Using a quantum work meter to test non-equilibrium fluctuation theorems
• Holevo's bound from a general quantum fluctuation theorem
• On the work distribution for the adiabatic compression of a dilute classical gas
• Construction of microcanonical entropy on thermodynamic pillars
• System-size scaling of Boltzmann and alternate Gibbs entropies
• Six out of equilibrium lectures
• Mechanical Proof of the Second Law of Thermodynamics Based on Volume Entropy
• Comment on "Consistent thermostatistics forbids negative absolute temperatures"
• Hyperspherical Treatment of Strongly-Interacting Few-Fermion Systems in One Dimension
• Reply to Schneider et al. [arXiv:1407.4127v1]

Cited by in corpus (1)

• Relations between entropy rate, entropy production and information geometry in linear stochastic systems