Dissipation and lag in irreversible processes

When a system is perturbed by the variation of external parameters, a lag generally develops between the actual state of the system and the equilibrium state corresponding to the current parameter values. We establish a microscopic, quantitative relation between this lag and the dissipated work that accompanies the process. We illustrate this relation using a model system.Comment: 6 pages, 3 figures, accepted for publication in EP

Equilibrium Free Energies from Nonequilibrium Processes

A recent result, relating the (irreversible) work performed on a system during a non-quasistatic process, to the Helmholtz free energy difference between two equilibrium states of the system, is discussed. A proof of this result is given for the special case when the evolution of the system in question is modelled by a Langevin equation in configuration space.Comment: Conference talk in Zakopane, Poland; 11 pages + 3 figure

A quantum version of free energy - irreversible work relations

We give a quantum version of the Jarzynski relation between the distribution of work done over a certain time-interval on a system and the difference of equilibrium free energies. The main new ingredient is the identification of work depending on the quantum history of the system and the proper definition of various quantum ensembles over which the averages should be made. We also discuss a number of different regimes that have been considered by other authors and which are unified in the present set-up. In all cases, and quantum or classical, it is a general relation between heat and time-reversal that makes the Jarzynski relation so universally valid

A "fast growth" method of computing free energy differences

Let Delta F be the free energy difference between two equilibrium states of a system. An established method of numerically computing Delta F involves a single, long ``switching simulation'', during which the system is driven reversibly from one state to the other (slow growth, or adiabatic switching). Here we study a method of obtaining the same result from numerous independent, irreversible simulations of much shorter duration (fast growth). We illustrate the fast growth method, computing the excess chemical potential of a Lennard-Jones fluid as a test case, and we examine the performance of fast growth as a practical computational tool.Comment: 17 pages + 4 figures, accepted for publication in J.Chem.Phy

Comment on: Failure of the Work-Hamiltonian Connection for Free-Energy Calculations [Phys Rev Lett 100, 020601 (2008), arXiv:0704.0761]

We comment on a Letter by Vilar and Rubi [arXiv:0704.0761].Comment: one page, including one figure; to appear in Phys Rev Let

A Quantum Analogue of the Jarzynski Equality

A quantum analogue of the Jarzynski equality is constructed. This equality connects an ensemble average of exponentiated work with the Helmholtz free-energy difference in a nonequilibrium switching process subject to a thermal heat bath. To confirm its validity in a practical situation, we also investigate an open quantum system that is a spin 1/2 system with a scanning magnetic field interacting with a thermal heat bath. As a result, we find that the quantum analogue functions well.Comment: 7 pages, 1 figure; to appear in J. Phys. Soc. Jpn. 69 (2000