We investigate how to coherently define entropy production for a process of transient relaxation in the quantum Brownian motion model for the harmonic potential. We compare a form, referred to as 'poised' (P), which after non-Markovian transients corresponds to a definition of heat as the change in the system Hamiltonian of mean force, with a recent proposal by Esposito et al (ELB) based on a definition of heat as the energy change in the bath. Both expressions yield a positive-definite entropy production and they coincide for vanishing coupling strength, but their difference is proved to be always positive (after non-Markovian transients disappear) and to grow as the coupling strength increases. In the classical over-damped limit the 'poised' entropy production converges to the entropy production used in stochastic thermodynamics. We also investigate the effects of the system size, and of the ensuing Poincaré recurrences, and how the classical limit is approached. We close by discussing the strong-coupling limit, in which the ideal canonical equilibrium of the bath is violated.
I investigate how to coherently define entropy production for a process of transient relaxation in the Quantum Brownian Motion model for the harmonic potential. I compare a form, called ``Poised" (P), which after non-Markovian transients corresponds to a definition of heat as the change in the system Hamiltonian of mean force, with a recent proposal by Esposito et al (ELB) based on a definition of heat as the energy change in the bath. Both expressions yield a positive-defined entropy production and coincide for vanishing coupling strength, but their difference is proved to be always positive (after non-Markovian transients disappear) and to grow as the coupling strength increases. In the classical over-damped limit the ``Poised" entropy production converges to the entropy production used in stochastic thermodynamics. We also investigate the effects of the system size, and of the ensuing Poincaré recurrences, and how the classical limit is approached. I close by discussing the strong-coupling limit, in which the ideal canonical equilibrium of the bath is violated.
We investigate the link between the irreversibility generated by a stationary dissipative process and the correlations established within a composite quantum system. We provide two equivalent expressions for the entropy generated in the non-equilibrium steady state of coupled quantum harmonic oscillators that allow for a simple interpretation of the onset of irreversibility. We then unveil a quantitative relation between the entropy production rate and correlations, both total and quantum, built between the two oscillators. In the small-coupling limit, the entropy production rate is shown to be proportional to both the mutual information and the quantum correlations. We apply our results to the analysis of the optomechanical interaction between a nano-mechanical resonator and a cavity field, and show that the behavior of the entropy production captures the peculiar features of the model, such as sideband cooling and amplification.
In this thesis we develop an approach to nonequilibrium quantum-statistical mechanics which is based on the consideration of the thermodynamic entropy as being a quantum observable with an associated hermitian operator and with its own equation of motion, from which the rate of entropy production can be studied. The relationship of this quantum observable---the expectation value of which is proved to obey the laws of thermodynamics and is thus called the thermodynamic entropy---with heat dissipation in quantum many-body systems is investigated in detail. After showing how the classical theory of nonequilibrium thermodynamics is obtained from our entropy-production formalism in the limit of very weakly coupled subsystems of a larger isolated quantum system, the solution of the equation of motion for the thermodynamic entropy operator is formally obtained and applied to the case of electrons interacting with phonons and being driven by an external electric field, arriving at an explicit expression for the Joule heat without any a priori consideration of the rate of change of the energy of the system. Finally, the formalism is applied to solve a puzzle introduced with the most basic model for atom-light interactions: the Jaynes-Cummings model. Without using the correct thermodynamic arguments implied by our entropy-production theory, this model leads to the conclusion that a stream of two-level atoms sent to a cavity filled with monochromatic photons---in the so called one-atom maser configuration---thermalize, under off-resonant conditions, to a temperature different from that of the photons, casting doubts on the validity of the principle of conservation of energy.
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.