Dynamic equations for three different qudits in a magnetic field

A closed system of equations for the local Bloch vectors and spin correlation functions of three magnetic qudits, which are in an arbitrary, time-dependent, external magnetic field, is obtained using decomplexification of the Liouville-von Neumann equation. The algorithm of the derivation of the dynamic equations is presented. In the basis convenient for the important physical applications structure constants of algebra su(2S+1) are calculated.Comment: 11 page

The absoption refrigerator as a thermal transformer

The absorption refrigerator can be considered a thermal transformer, i.e. a device that is analogous to the electric transformer. The analogy is based on a correspondence between the extensive quantities entropy and electric charge and that of the intensive variables temperature and electric potential

Efficiency at maximum power output of an irreversible Carnot-like cycle with internally dissipative friction

We investigate the efficiency at maximum power of an irreversible Carnot engine performing finite-time cycles between two reservoirs at temperatures $T_h$ and $T_c$ $(T_c<T_h)$, taking into account of internally dissipative friction in two "adiabatic" processes. In the frictionless case, the efficiencies at maximum power output are retrieved to be situated between $\eta_{_C}/$ and $\eta_{_C}/(2-\eta_{_C})$, with $\eta_{_C}=1-T_c/{T_h}$ being the Carnot efficiency. The strong limits of the dissipations in the hot and cold isothermal processes lead to the result that the efficiency at maximum power output approaches the values of $\eta_{_C}/$ and $\eta_{_C}/(2-\eta_{_C})$, respectively. When dissipations of two isothermal and two adiabatic processes are symmetric, respectively, the efficiency at maximum power output is founded to be bounded between 0 and the Curzon-Ahlborn (CA) efficiency $1-\sqrt{1-\eta{_C}}$, and the the CA efficiency is achieved in the absence of internally dissipative friction

Thermodynamic Bounds on Efficiency for Systems with Broken Time-reversal Symmetry

We show that for systems with broken time-reversal symmetry the maximum efficiency and the efficiency at maximum power are both determined by two parameters: a "figure of merit" and an asymmetry parameter. In contrast to the time-symmetric case, the figure of merit is bounded from above; nevertheless the Carnot efficiency can be reached at lower and lower values of the figure of merit and far from the so-called strong coupling condition as the asymmetry parameter increases. Moreover, the Curzon-Ahlborn limit for efficiency at maximum power can be overcome within linear response. Finally, always within linear response, it is allowed to have simultaneously Carnot efficiency and non-zero power.Comment: Final version, 4 pages, 3 figure

Quantum mechanical Carnot engine

A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing an ideal gas. Here, we present an example of a cyclic engine based on a single quantum-mechanical particle confined to a potential well. The efficiency of this engine is shown to equal the Carnot efficiency because quantum dynamics is reversible. The quantum heat engine has a cycle consisting of adiabatic and isothermal quantum processes that are close analogues of the corresponding classical processes.Comment: 10 page

Intrinsic Periodicity of Time and Non-maximal Entropy of Universe

The universe is certainly not yet in total thermodynamical equilibrium,so clearly some law telling about special initial conditions is needed. A universe or a system imposed to behave periodically gets thereby required ``initial conditions". Those initial conditions will \underline{not} look like having already suffered the heat death, i.e. obtained the maximal entropy, like a random state. The intrinsic periodicity explains successfully why entropy is not maximal, but fails phenomenologically by leading to a \underline{constant}entropy.Comment: 8 page

Efficiency of a thermodynamic motor at maximum power

Several recent theories address the efficiency of a macroscopic thermodynamic motor at maximum power and question the so-called "Curzon-Ahlborn (CA) efficiency." Considering the entropy exchanges and productions in an n-sources motor, we study the maximization of its power and show that the controversies are partly due to some imprecision in the maximization variables. When power is maximized with respect to the system temperatures, these temperatures are proportional to the square root of the corresponding source temperatures, which leads to the CA formula for a bi-thermal motor. On the other hand, when power is maximized with respect to the transitions durations, the Carnot efficiency of a bi-thermal motor admits the CA efficiency as a lower bound, which is attained if the duration of the adiabatic transitions can be neglected. Additionally, we compute the energetic efficiency, or "sustainable efficiency," which can be defined for n sources, and we show that it has no other universal upper bound than 1, but that in certain situations, favorable for power production, it does not exceed 1/2

Driven Spin Systems as Quantum Thermodynamic Machines: Fundamental Limits

We show that coupled two level systems like qubits studied in quantum information can be used as a thermodynamic machine. At least three qubits or spins are necessary and arranged in a chain. The system is interfaced between two split baths and the working spin in the middle is externally driven. The machine performs Carnot-type cycles and is able to work as heat pump or engine depending on the temperature difference of the baths $\Delta T$ and the energy differences in the spin system $\Delta E$. It can be shown that the efficiency is a function of $\Delta T$ and $\Delta E$.Comment: 9 pages, 11 figures, accepted for publication in Phys. Rev.

Efficiency at maximum power of thermally coupled heat engines

We study the efficiency at maximum power of two coupled heat engines, using thermoelectric generators (TEGs) as engines. Assuming that the heat and electric charge fluxes in the TEGs are strongly coupled, we simulate numerically the dependence of the behavior of the global system on the electrical load resistance of each generator in order to obtain the working condition that permits maximization of the output power. It turns out that this condition is not unique. We derive a simple analytic expression giving the relation between the electrical load resistance of each generator permitting output power maximization. We then focuse on the efficiency at maximum power (EMP) of the whole system to demonstrate that the Curzon-Ahlborn efficiency may not always be recovered: the EMP varies with the specific working conditions of each generator but remains in the range predicted by irreversible thermodynamics theory. We finally discuss our results in light of non-ideal Carnot engine behavior.Comment: 11 pages, 7 figure

Irreversible Performance of a Quantum Harmonic Heat Engine

The unavoidable irreversible losses of power in a heat engine are found to be of quantum origin. Following thermodynamic tradition a model quantum heat engine operating by the Otto cycle is analyzed. The working medium of the model is composed of an ensemble of harmonic oscillators. A link is established between the quantum observables and thermodynamical variables based on the concept of canonical invariance. These quantum variables are sufficient to determine the state of the system and with it all thermodynamical variables. Conditions for optimal work, power and entropy production show that maximum power is a compromise between the quasistatic limit of adiabatic following on the compression and expansion branches and a sudden limit of very short time allocation to these branches. At high temperatures and quasistatic operating conditions the efficiency at maximum power coincides with the endoreversible result. The optimal compression ratio varies from the square root of the temperature ratio in the quasistatic limit where their reversibility is dominated by heat conductance to the temperature ratio to the power of 1/4 in the sudden limit when the irreversibility is dominated by friction. When the engine deviates from adiabatic conditions the performance is subject to friction. The origin of this friction can be traced to the noncommutability of the kinetic and potential energy of the working medium.Comment: 25 pages, 7 figures. Revision added explicit heat-transfer expression and extended the discussion on the quantum origin of frictio