Cooling by heating: Restoration of the third law of thermodynamics.

We have made a simple and natural modification of a recent quantum refrigerator model presented by Cleuren et al. [Phys. Rev. Lett. 108, 120603 (2012)]. The original model consist of two metal leads acting as heat baths and a set of quantum dots that allow for electron transport between the baths. It was shown to violate the dynamic third law of thermodynamics (the unattainability principle, which states that cooling to absolute zero in finite time is impossible). By taking into consideration the finite energy level spacing Δ, in metals we restore the third law while keeping all of the original model's thermodynamic properties intact down to the limit of k(B)T ∼ Δ, where the cooling rate is quenched. The spacing Δ depends on the confinement of the electrons in the lead and therefore, according to our result larger samples (with smaller level spacing), could be cooled efficiently to lower absolute temperatures than smaller ones. However, a large lead makes the assumption of instant equilibration of electrons implausible; in reality one would only cool a small part of the sample and we would have a nonequilibrium situation. This property is expected to be model independent and raises the question whether we can find an optimal size for the lead that is to be cooled.

Dephasing and dissipation in qubit thermodynamics.

We analyze the stochastic evolution and dephasing of a qubit within the quantum jump approach. It allows one to treat individual realizations of inelastic processes, and in this way it provides solutions, for instance, to problems in quantum thermodynamics and distributions in statistical mechanics. We demonstrate that dephasing and relaxation of the qubit render the Jarzynski and Crooks fluctuation relations (FRs) of nonequilibrium thermodynamics intact. On the contrary, the standard two-measurement protocol, taking into account only the fluctuations of the internal energy U, leads to deviations in FRs under the same conditions. We relate the average 〈e(-ßU)〉 (where ß is the inverse temperature) with the qubit's relaxation and dephasing rates in the weak dissipation limit and discuss this relationship for different mechanisms of decoherence.

Information flow and optimal protocol for a Maxwell-demon single-electron pump.

We study the entropy and information flow in a Maxwell-demon device based on a single-electron transistor with controlled gate potentials. We construct the protocols for measuring the charge states and manipulating the gate voltages, which minimizes irreversibility for (i) constant input power from the environment or (ii) given energy gain. Charge measurement is modeled by a series of detector readouts for time-dependent gate potentials, and the amount of information obtained is determined. The protocols optimize irreversibility that arises due to (i) enlargement of the configuration space on opening the barriers, and (ii) finite rate of operation. These optimal protocols are general and apply to all systems in which barriers between different regions can be manipulated.

Experimental demonstration of Snell's law for shear zone refraction in granular materials.

We present experiments on slow shear flow in granular materials. Under appropriate conditions shear localizes in narrow shear zones. We demonstrate that when the shear zone crosses a material boundary, it refracts in accordance with Snell's law in optics-an effect first found in simulations [Phys. Rev. Lett. 98, 018301 (2007)]. The shear zone is the one that minimizes the dissipation rate upon shearing, i.e., a manifestation of the principle of least dissipation. We have prepared the materials as to form a granular lens. Shearing through the lens is shown to give a very broad shear zone, which corresponds to fulfilling Snell's law for a continuous range of paths through the cell.

Non-Gaussian low-frequency noise as a source of qubit decoherence.

We study decoherence in a qubit with the distance between the two levels affected by random flips of bistable fluctuators. For the case of a single fluctuator we evaluate explicitly an exact expression for the phase-memory decay in the echo experiment with a resonant ac excitation. The echo signal as a function of time shows a sequence of plateaus. The position and the height of the plateaus can be used to extract the fluctuator switching rate gamma and its coupling strength v. At small times the logarithm of the echo signal is proportional to t3. The plateaus disappear when the decoherence is induced by many fluctuators. In this case the echo signal depends on the distribution of the fluctuators parameters. According to our analysis, the results significantly deviate from those obtained in the Gaussian model as soon as v greater than or approximately equal gamma.