As stated by the second law of thermodynamics, the irreversible entropy of a system keeps being produced until it reaches the equilibrium, and the entropy production rate is always non-negative. But when some exotic quantum properties, e.g., quantum coherence or squeezing, exist in the bath, it has been reported that the 2nd law does not apply. Correspondingly, the previous description of the entropy production rate does not apply either, and it is not always non-negative in these cases. We notice that the entropy production rate can be generalized to be the increasing rate of the mutual information between the open system and its environment. For thermal baths, this mutual information production rate equals to the previous entropy production rate. For non-thermal baths, in an example of a single boson mode interacting with multiple squeezed thermal baths, we proved that the mutual information production rate is always non-negative. The monotonic increasing mutual information means the system and its environment are becoming more and more correlated during the evolution.
As stated by the second law of thermodynamics, the irreversible entropy of a system keeps being produced until it reaches the equilibrium, and the entropy production rate is always non-negative. But when some exotic quantum properties, e.g., quantum coherence or squeezing, exist in the bath, it has been reported that the 2nd law does not apply. Correspondingly, the previous description of the entropy production rate does not apply either, and it is not always non-negative in these cases. We notice that the entropy production rate can be generalized to be the increasing rate of the mutual information between the open system and its environment. For thermal baths, this mutual information production rate equals to the previous entropy production rate. For non-thermal baths, in an example of a single boson mode interacting with multiple squeezed thermal baths, we proved that the mutual information production rate is always non-negative. The monotonic increasing mutual information means the system and its environment are becoming more and more correlated during the evolution.
When an open system comes into contact with several thermal baths, the entropy produced by the irreversible processes (dS_{i}=dS-∑_{α} đQ_{α}/T_{α}) keeps increasing, and this entropy production rate is always non-negative. However, when the system comes into contact with nonthermal baths containing quantum coherence or squeezing, this entropy production formula does not apply. In this paper, we study the increasing rate of mutual information between an open system and its environment. In the case of canonical thermal baths, we prove that this mutual information production rate could return exactly to the previous entropy production rate. Furthermore, we study an example of a single boson mode that comes into contact with multiple squeezed thermal baths, where the conventional entropy production rate does not apply, and we find that this mutual information production rate remains non-negative, which indicates a monotonic increase in the correlation between the system and its environment.
The Markovian time evolution of the entropy production rate is studied as a measure of irreversibility generated in a bipartite quantum system consisting of two coupled bosonic modes immersed in a common thermal environment. The dynamics of the system is described in the framework of the formalism of the theory of open quantum systems based on completely positive quantum dynamical semigroups, for initial two-mode squeezed thermal states, squeezed vacuum states, thermal states and coherent states. We show that the rate of the entropy production of the initial state and nonequilibrium stationary state, and the time evolution of the rate of entropy production, strongly depend on the parameters of the initial Gaussian state (squeezing parameter and average thermal photon numbers), frequencies of modes, parameters characterising the thermal environment (temperature and dissipation coefficient), and the strength of coupling between the two modes. We also provide a comparison of the behaviour of entropy production rate and Rényi-2 mutual information present in the considered system.
According to the first and second laws of thermodynamics and the definitions of work and heat, microscopic expressions for the non-equilibrium entropy production have been achieved. Recently, a redefinition of heat has been presented in [Nature Communications volume 8, Article number: 2180 (2017)]. Since thermal operations play an important role in the resource theory of thermodynamics, it would be very interesting to find out the effect of the above-mentioned definition on the expression of the entropy production for these kind of operations. This is one of the aims of the present paper. Using the new definition of heat, it is shown that the entropy production is the same as the mutual information between a system and a bath both for thermal operations and, if the system-bath initial state is factorized, for entropy-preserving operations. It is also discussed that how one can recognize the type of the correlation between a system and a bath through knowledge of the initial state of the system only. It is shown that if the initial state of a system is diagonal in the energy basis, the thermal operations cannot create a quantum correlation between the system and the bath, however, if the system initial state is coherent Gibbs state, there cannot be classical correlation due to the thermal operations.
Thermodynamics is a phenomenological theory describing the energy conversion of work and heat. At its origins thermodynamics was developed in order to understand and improve heat engines. In conventional thermodynamics, however, only such processes are completely describable which are slow enough to keep the system of interest in an equilibrium state with its thermal environment at all times. On the contrary, all real physical processes are accompanied by non-equilibrium phenomena. These are mathematically described with the help of the irreversible entropy production, i.e. the dissipated work divided by the temperature of the bath. The second law of thermodynamics merely states that the irreversible entropy production is on average always positive. The modern trend of miniaturization, however, leads to smaller and smaller devices. On short length scales thermal noise as well as quantum fluctuations become important. Thus, usual thermodynamic quantities as work and heat acquire stochastic nature. Moreover, in the quantum regime a completely new theory had to be invented, since classical notions of work and heat are no longer valid. The present dissertation contributes to this prevailing field by the derivation of analytical expressions for the entropy production in open and closed quantum system far from thermal equilibrium. The theoretical treatment is motivated by an experimental point of view. The obtained results were derived from the reduced dynamics of the quantum mechanical system, which may be coupled to a thermal bath. To this end, it was dealt with methods and approaches of statistical physics, conventional thermodynamics, quantum information theory and the theory of open quantum systems. In this dissertation the most important physical systems are treated. First, an isolated system is considered before later on a heat bath is included. The limit of weak as well as of strong coupling are analyzed in detail. For isolated systems it turns out that a geometric approach is able to capture the thermodynamic properties, completely. To this end, the irreversible entropy production is sharply estimated from below by the angle between the real non-equilibrium state and the corresponding equilibrium one. Further, it is shown that the Heisenberg uncertainty relation for energy and time can be formulated more precisely in terms of that angle. As experimental system cold ion traps are introduced, in which the theoretical predictions can be verified. For weakly coupled systems, then, the irreversible entropy production is identified and a fluctuation theorem is derived by merely thermodynamic arguments. As experimental system we, again, propose the cold ion traps, where the heat bath can be simulated with the help of LASER light. In the limit of strong coupling a semiclassical description of the reduced quantum system is discussed. Again, an analytically exact expression for the entropy production and the corresponding fluctuation theorem is derived. A physical system, in which strong coupling to the environment can be analyzed, is given by Josephson junctions. This dissertation discusses the entropy production for isolated, weakly coupled, and overdamped quantum systems. For these physical regimes analytical relation are derived and experimental systems proposed, with which the predictions can be verified.
Entropy production plays a fundamental role in nonequilibrium thermodynamics to quantify the irreversibility of open systems. Its positivity can be ensured for a wide class of setups, but the entropy production rate can become negative sometimes. This is often taken as an indicator of non-Markovianity. We make this link precise by showing under which conditions a negative entropy production rate implies non-Markovianity and when it does not. For a system coupled to a single heat bath, this can be established within a unified language for two setups: (i) the dynamics resulting from a coarse-grained description of a Markovian master equation and (ii) the classical Hamiltonian dynamics of a system coupled to a bath. The quantum version of the latter result is shown not to hold despite the fact that the integrated thermodynamic description is formally equivalent to the classical case. The instantaneous fixed point of a non-Markovian dynamics plays an important role in our study. Our key contribution is to provide a consistent theoretical framework to study the finite-time thermodynamics of a large class of dynamics with a precise link to its non-Markovianity.
Entropy production is the key quantity behind the second law of thermodynamics, and it is well defined by considering a joint unitary evolution of a system S and a thermal environment E. However, due to the diversity of initial state and Hamiltonian of S and E, it is hard to evaluate the characterization of the entropy production. In this Letter we propose that the evolution of S and E can be solved non-perturbatively in the framework of Gaussian quantum mechanics (GQM) for Gaussian states and quadratic Hamiltonian. We study the entropy production and correlation spreading in two models of E: one-dimensional free massless scalar quantum field theory in a cavity and an oscillator chain with adjacent interactions. The result is not what one might naively expect, S being thermalized and keeps stable, but is all the physical quantities, such as entropy production, mutual information, and the effective temperature of S, are fluctuating. In general the interaction between S and E creates correlation, and this correlation could spread in E and cause the physical quantities to fluctuate. The detailed information depends on the coupling strength, number of modes, boundary condition and other parameters. This analysis can be extended to any other models in the framework of QGM.