Synopsis: Quantum Pistons

Calculations reveal the relationship between work and free energy for a quantum particle contained in a box with a moving wall.
Synopsis figure
C. Jarzynski and H. T. Quan, Phys. Rev. E (2012)

In equilibrium, the change in free energy, ΔF, of a system as it transitions between two states sets a limit on the work, W, that can be realized in the process. Theorists have searched for similar exact relations between the work done on or by a system and its change in free energy in nonequilibrium processes, and some of these relations have been verified in experiments on small, effectively classical systems, such as macromolecules.

Showing the relations are also valid in nonequilibrium quantum systems is of fundamental importance. A case in point is the “Jarzynski equality” derived by Christopher Jarzynski at the University of Maryland, College Park, which states that, classically, the statistical average of exp[-W/KBT] is equivalent to exp[-ΔF/KBT]. Whether the equality applies to a quantum piston—a quantum particle in a one-dimensional box, with one of the walls moving at a fixed velocity—has remained an open question.

Writing in Physical Review E, Jarzynski and Haitao Quan, also at the University of Maryland, utilize a solution to the time-dependent Schrödinger equation for this quantum machine that shows the Jarzynski equality is in fact satisfied. Their result is not intuitively obvious, as there are important differences between the classical and quantum pistons; for example, the work performed on a classical particle is always negative in an expanding piston, but quantum fluctuations lead to the possibility of positive work in the quantum case. – Ronald Dickman


More Features »


More Announcements »

Subject Areas

Quantum PhysicsStatistical Physics

Previous Synopsis

Biological Physics

Fractal Teeth

Read More »

Next Synopsis

Nonlinear Dynamics

Lévy Flight of the Bumblebee

Read More »

Related Articles

Synopsis: Direct View of Exchange Symmetry
Quantum Physics

Synopsis: Direct View of Exchange Symmetry

A proposed set of experiments could offer a direct measurement of the fundamental quantum property that distinguishes fermions from bosons. Read More »

Viewpoint: Squeezed Environment Boosts Engine Performance

Viewpoint: Squeezed Environment Boosts Engine Performance

A tiny engine can surpass the Carnot limit of efficiency when researchers engineer the thermal properties of the environment. Read More »

Synopsis: Subway Stats
Statistical Physics

Synopsis: Subway Stats

A comparison of the arrival-time statistics of New York City’s subway trains indicates that some train lines may be more efficiently run than others. Read More »

More Articles