C. Van den Broeck

Dissipation: The Phase-Space Perspective

We show, through a refinement of the work theorem, that the average dissipation, upon perturbing a Hamiltonian system arbitrarily far out of equilibrium in a transition between two canonical equilibrium states, is exactly given by =W-DeltaF=kTD(rho||rho[over ])=kT, where rho and rho[over ] are the phase-space density of the system measured at the same intermediate but otherwise arbitrary point in time, for the forward and backward process. D(rho||rho[over ]) is the relative entropy of rho versus rho[over ]. This result also implies general inequalities, which are significantly more accurate than the second law and include, as a special case, the celebrated Landauer principle on the dissipation involved in irreversible computations.

Thermoelectric efficiency at maximum power in a quantum dot

We identify the operational conditions for maximum power of a nanothermoelectric engine consisting of a single quantum level embedded between two leads at different temperatures and chemical potentials. The corresponding thermodynamic efficiency agrees with the Curzon-Ahlborn expression up to quadratic terms in the gradients, supporting the thesis of universality beyond linear response.

Second law and Landauer principle far from equilibrium

The amount of work that is needed to change the state of a system in contact with a heat bath between specified initial and final nonequilibrium states is at least equal to the corresponding equilibrium free energy difference plus (respectively, minus) temperature times the information of the final (respectively, the initial) state relative to the corresponding equilibrium distributions.

Entropy production and the arrow of time

We present an exact relationship between the entropy production and the distinguishability of a process from its time-reverse, quantified by the relative entropy between forward and backward states. The relationship is shown to remain valid for a wide family of initial conditions, such as canonical, constrained canonical, multi-canonical and grand canonical distributions, as well as both for classical and quantum systems.

Ensemble and trajectory thermodynamics: A brief introduction

We revisit stochastic thermodynamics for a system with discrete energy states in contact with a heat and particle reservoir.

Finite-time thermodynamics for a single level quantum dot

We investigate the finite-time thermodynamics of a single-level fermion system interacting with a particle reservoir. The optimal protocol to extract the maximum work from the system when moving the single energy level between an initial higher value and a final lower value in a finite time is calculated from a quantum master equation. The calculation also yields the optimal protocol to raise the energy level with the expenditure of the least amount of work on the system. The optimal protocol displays discontinuous jumps at the initial and final times.

Fluctuation and dissipation of work in a joule experiment

We elucidate the connection between various fluctuation theorems by a microcanonical version of the Crooks relation. We derive the microscopically exact expression for the work distribution in an idealized Joule experiment, namely, for a convex object moving at constant speed through an ideal gas. Analytic results are compared with molecular dynamics simulations of a hard disk gas.

A stochastic description of longitudinal dispersion in uniaxial flows

The time dependent longitudinal dispersion of Brownian particles, suspended in a fluid in unidirectional steady or oscillatory motion is calculated on the basis of the equivalence of Langevin and Fokker-Planck formalisms. In particular, a series expansion for the effective longitudinal diffusion coefficient is obtained. The method is applied to flows between plane parallel plates and flows in a cylindrical tube.

Lower bounds on dissipation upon coarse graining

By different coarse-graining procedures, we derive lower bounds on the total mean work dissipated in Brownian systems driven out of equilibrium. With several analytically solvable examples, we illustrate how, when, and where the information on the dissipation is captured.

Jarzynski equality for the Jepsen gas

We illustrate the Jarzynski equality on the exactly solvable model of an ideal gas in uniform expansion or compression. The analytical results for the probability density P(W) of the work W performed by the gas are compared with the results of molecular dynamics simulations for a two-dimensional dilute gas of hard spheres, a prototype for a real, slightly non-ideal gas.