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.Comment: Course given by C. Van den Broeck at the Summer School "Fundamental Problems in Statistical Physics XIII", June 16-29, 2013 Leuven, Belgium; V2: version accepted in Physica A (references improved + other minor changes

Reliable and timely event notification for publish/subscribe services over the internet

The publish/subscribe paradigm is gaining attention for the development of several applications in wide area networks (WANs) due to its intrinsic time, space, and synchronization decoupling properties that meet the scalability and asynchrony requirements of those applications. However, while the communication in a WAN may be affected by the unpredictable behavior of the network, with messages that can be dropped or delayed, existing publish/subscribe solutions pay just a little attention to addressing these issues. On the contrary, applications such as business intelligence, critical infrastructures, and financial services require delivery guarantees with strict temporal deadlines. In this paper, we propose a framework that enforces both reliability and timeliness for publish/subscribe services over WAN. Specifically, we combine two different approaches: gossiping, to retrieve missing packets in case of incomplete information, and network coding, to reduce the number of retransmissions and, consequently, the latency. We provide an analytical model that describes the information recovery capabilities of our algorithm and a simulation-based study, taking into account a real workload from the Air Traffic Control domain, which evidences how the proposed solution is able to ensure reliable event notification over a WAN within a reasonable bounded time window. © 2013 IEEE

Three detailed fluctuation theorems

The total entropy production of a trajectory can be split into an adiabatic and a non-adiabatic contribution, deriving respectively from the breaking of detailed balance via nonequilibrium boundary conditions or by external driving. We show that each of them, the total, the adiabatic and the non-adiabatic trajectory entropy, separately satisfies a detailed fluctuation theorem.Comment: 4 pages, V2: accepted in Phys. Rev. Lett. 104, 090601 (2010

Work statistics in stochastically driven systems

We identify the conditions under which a stochastic driving inducing energy changes on a system coupled to a thermal bath can be treated as a work source. When these conditions are met, the work statistics satisfies the Crooks fluctuation theorem traditionally derived for deterministic drivings. We illustrate this fact by calculating and comparing the work statistics for a two-level system driven respectively by a stochastic and a deterministic piecewise constant protocol.Comment: 19 pages, 7 figures, 2 table

Universal theory of efficiency fluctuations

Using the fluctuation theorem supplemented with geometric arguments, we derive universal features of the (long-time) efficiency fluctuations for thermal and isothermal machines operating under steady or periodic driving, close or far from equilibrium. In particular, the long-time probability for observing a reversible efficiency in a given engine is identical to that for the same engine working under the time-reversed driving. When the driving is symmetric, this reversible efficiency becomes the least probable.Comment: 10 pages, 9 figures, 1 tabl

The unlikely Carnot efficiency

The efficiency of an heat engine is traditionally defined as the ratio of its average output work over its average input heat. Its highest possible value was discovered by Carnot in 1824 and is a cornerstone concept in thermodynamics. It led to the discovery of the second law and to the definition of the Kelvin temperature scale. Small-scale engines operate in the presence of highly fluctuating input and output energy fluxes. They are therefore much better characterized by fluctuating efficiencies. In this study, using the fluctuation theorem, we identify universal features of efficiency fluctuations. While the standard thermodynamic efficiency is, as expected, the most likely value, we find that the Carnot efficiency is, surprisingly, the least likely in the long time limit. Furthermore the probability distribution for the efficiency assumes a universal scaling form when operating close-to-equilibrium. We illustrate our results analytically and numerically on two model systems.Comment: 7 pages, 3 figures, v3: as accepted in Nature Communication

Quantum-dot Carnot engine at maximum power

We evaluate the efficiency at maximum power of a quantum-dot Carnot heat engine. The universal value of the coefficients at the linear and quadratic order in the temperature gradient are reproduced. Curzon-Ahlborn efficiency is recovered in the limit of weak dissipation.Comment: 6 pages, 1 figur

Universality of efficiency at maximum power

We investigate the efficiency of power generation by thermo-chemical engines. For strong coupling between the particle and heat flows and in the presence of a left-right symmetry in the system, we demonstrate that the efficiency at maximum power displays universality up to quadratic order in the deviation from equilibrium. A maser model is presented to illustrate our argument.Comment: 4 pages, 2 figure

Stochastically driven single level quantum dot: a nano-scale finite-time thermodynamic machine and its various operational modes

We describe a single-level quantum dot in contact with two leads as a nanoscale finite-time thermodynamic machine. The dot is driven by an external stochastic force that switches its energy between two values. In the isothermal regime, it can operate as a rechargeable battery by generating an electric current against the applied bias in response to the stochastic driving, and re-delivering work in the reverse cycle. This behavior is reminiscent of the Parrondo paradox. If there is a thermal gradient the device can function as a work-generating thermal engine, or as a refrigerator that extracts heat from the cold reservoir via the work input of the stochastic driving. The efficiency of the machine at maximum power output is investigated for each mode of operation, and universal features are identified.Comment: 4 pages, 3 figures, V2: typos corrected around eq.(12