Single Heat Bath Research Articles

Stochastic thermodynamics with information reservoirs.

We generalize stochastic thermodynamics to include information reservoirs. Such information reservoirs, which can be modeled as a sequence of bits, modify the second law. For example, work extraction from a system in contact with a single heat bath becomes possible if the system also interacts with an information reservoir. We obtain an inequality, and the corresponding fluctuation theorem, generalizing the standard entropy production of stochastic thermodynamics. From this inequality we can derive an information processing entropy production, which gives the second law in the presence of information reservoirs. We also develop a systematic linear response theory for information processing machines. For a unicyclic machine powered by an information reservoir, the efficiency at maximum power can deviate from the standard value of 1/2. For the case where energy is consumed to erase the tape, the efficiency at maximum erasure rate is found to be 1/2.

Optimized finite-time information machine

We analyze a periodic optimal finite-time two-state information-driven machine that extracts work from a single heat bath exploring imperfect measurements. Two models are considered, a memory-less one that ignores past measurements and an optimized model for which the feedback scheme consists of a protocol depending on the whole history of measurements. Depending on the precision of the measurement and on the period length, the optimized model displays a phase transition to a phase where measurements are judged as non-reliable. We obtain the critical line exactly and show that the optimized model leads to more work extraction in comparison to the memory-less model, with the gain parameter being larger in the region where the frequency of non-reliable measurements is higher. We also demonstrate that the model has two second law inequalities, with the extracted work being bounded by the change of the entropy of the system and by the mutual information.

Extracting work from a single heat bath: a case study of a Brownian particle under an external magnetic field in the presence of information.

Work can be extracted from a single bath beyond the limit set by the second law of thermodynamics by performing measurement on the system and utilizing the acquired information. This imposes an upper bound on extracted work and maintains a generalized (i.e., with information) second law. As an example, we studied a Brownian particle confined in a two-dimensional harmonic trap in the presence of a magnetic field, whose position coordinates are measured with finite precision. Two separate cases are investigated in this study: (A) moving the center of the potential and (B) varying the stiffness of the potential. Optimal protocols that extremize the work in a finite-time process are explicitly calculated for these two cases. For case A, we show that even though the optimal protocols depend on magnetic field, surprisingly, extracted work is independent of the field. For case B, both the optimal protocol and the extracted work depend on the magnetic field. However, the presence of a magnetic field always reduces the extraction of work for the latter case.

Thermodynamic cost of measurements

The measurement of thermal fluctuations provides information about the microscopic state of a thermodynamic system and can be used in order to extract work from a single heat bath in a suitable cyclic process. We present a minimal framework for the modeling of a measurement device and we propose a protocol for the measurement of thermal fluctuations. In this framework, the measurement of thermal fluctuations naturally leads to the dissipation of work. We illustrate this framework on a simple two states system inspired by the Szilard's information engine.

Cooling Classical Particles with a Microcanonical Szilard Engine

The possibility of extracting energy from a system in a cyclic process is discussed. We present an explicit example where a system, initially prepared in a microcanonical state, is able to perform such an operation. The example is similar to the Szilard engine, but the microcanonical initial condition allows one to design a protocol where measurement is not necessary.

Specific heat anomalies of open quantum systems

The evaluation of the specific heat of an open damped quantum system is a subtle issue. One possible route is based on the thermodynamic partition function which is the ratio of the partition functions of system plus bath and of the bath alone. For the free damped particle it has been shown, however, that the ensuing specific heat may become negative for appropriately chosen environments. Being an open system this quantity then naturally must be interpreted as the change in the specific heat obtained as the difference between the specific heat of the heat bath coupled to the system degrees of freedom and the specific heat of the bath alone. While this difference may become negative, the involved specific heats themselves are always positive; thus, the known thermodynamic stability criteria are perfectly guaranteed. For a damped quantum harmonic oscillator, instead of negative values, under appropriate conditions one can observe a dip in the difference of specific heats as a function of temperature. Stylized minimal models containing a single oscillator heat bath are employed to elucidate the occurrence of the anomalous temperature dependence of the corresponding specific heat values. Moreover, we comment on the consequences for the interpretation of the density of states based on the thermal partition function.

Fluctuation relations in non-equilibrium stationary states of Ising models

Fluctuation relations for the entropy production in non-equilibrium stationary states ofIsing models are investigated by means of Monte Carlo simulations. Systems in contactwith heat baths at two different temperatures or subject to external driving will bestudied. In the first case, considering different kinetic rules and couplings with thebaths, the behaviors of the probability distributions of the heat exchanged in timeτ with the thermostats, both in the disordered phase and in the low temperaturephase, are discussed. The fluctuation relation is always followed in the largeτ limit and deviations from linear response theory are observed. Finiteτ corrections are shown to obey a scaling behavior. In the other case the system is in contactwith a single heat bath, but work is done by shearing it. Also for this system, using thestatistics collected for the mechanical work we show the validity of the fluctuation relationand the preasymptotic corrections behave analogously to those for the case with two baths.

Dissipative quantum oscillator with two competing heat baths

We study the dissipative dynamics of a harmonic oscillator which couples linearly through its position and its momentum to two independent heat baths at the same temperature. We argue that this model describes a large spin in a ferromagnet. We find that some effects of the two heat baths partially cancel each other. This leads to unexpected features such as underdamped oscillations and long relaxation times in the strong coupling regime. Such a partial frustration of dissipation can be ascribed to the canonically conjugate character of position and momentum. We compare this model to the scenario where a single heat bath couples linearly to both the position and the momentum of the central oscillator. In that case less surprising behaviour occurs for strong coupling. The dynamical evolution of the quantum purity for a single and a double wave packet is also investigated.

Extracting work from a single heat bath via vanishing quantum coherence.

We present here a quantum Carnot engine in which the atoms in the heat bath are given a small bit of quantum coherence. The induced quantum coherence becomes vanishingly small in the high-temperature limit at which we operate and the heat bath is essentially thermal. However, the phase phi, associated with the atomic coherence, provides a new control parameter that can be varied to increase the temperature of the radiation field and to extract work from a single heat bath. The deep physics behind the second law of thermodynamics is not violated; nevertheless, the quantum Carnot engine has certain features that are not possible in a classical engine.

Isothermal ratchets: Numerical study of the efficiency of the energy transduction

The energetics of isothermal ratchets, that are driven by an external force and operate in contact with a single heat bath, is studied by Langevin equation simulations. The system is analyzed in terms of the mass, friction and amplitude of the external forcing. We found a regime where the efficiency is optimized at finite temperatures, proving that thermal fluctuations facilitate the efficiency of the energy conversion. The condition of optimal efficiency is found, relating mass, temperature and friction to the properties of the ratchet potential.

Energy transduction of isothermal ratchets: generic aspects and specific examples close to and far from equilibrium.

We study the energetics of isothermal ratchets which are driven by a chemical reaction between two states, and operate in contact with a single heat bath of constant temperature. We discuss generic aspects of energy transduction such as Onsager relations in the linear response regime as well as the efficiency and dissipation close to and far from equilibrium. In the linear response regime where the system operates reversibly, the efficiency is in general nonzero. Studying the properties for specific examples of energy landscapes and transitions, we observe in the linear response regime that the efficiency can have a maximum as a function of temperature. Far from equilibrium in the fully irreversible regime, we find a maximum of the efficiency with values larger than in the linear regime for an optimal choice of the chemical driving force. We show that the corresponding efficiencies can be of the order of 50%. A simple analytic argument allows us to estimate the efficiency in this irreversible regime for small external forces.