We show that the quantum statistical mechanics (QSM) describing quantum and thermal properties of objects has only the sense of a particular semiclassical approximation. We propose a more general (than QSM) micro description of objects in a heat bath taken into account a vacuum as an object environment; we call it ( ħ, k )-dynamics ( ħkD ). We construct a new model of thermostat, namely, a quantum heat bath and study its properties including the cases of a “cold” and “thermal” vacua. We introduce a new generative operator, Schroedingerian, or stochastic action operator, and show its fundamental role in the determination such macro-quantities as internal energy, effective temperature, and effective entropy. We establish that in ħkD the ratio of effective action to effective entropy at zero temperature equals the universal constant ħ /2 k . This result corresponds to experimental data taken recently under studying of a new matter state—nearly perfect fluid.
We show that the quantum statistical mechanics (QSM) describing quantum and thermal properties of objects has only the sense of a particular semiclassical approximation. We propose a more general (than QSM) micro description of objects in a heat bath taken into account a vacuum as an object environment; we call it ( ħ, k )-dynamics ( ħkD ). We construct a new model of thermostat, namely, a quantum heat bath and study its properties including the cases of a “cold” and “thermal” vacua. We introduce a new generative operator, Schroedingerian, or stochastic action operator, and show its fundamental role in the determination such macro-quantities as internal energy, effective temperature, and effective entropy. We establish that in ħkD the ratio of effective action to effective entropy at zero temperature equals the universal constant ħ /2 k . This result corresponds to experimental data taken recently under studying of a new matter state—nearly perfect fluid.
We suggest a more general than quantum statistical mechanics (QSM) microdescription of objects in a heat bath taken into account a vacuum as an object environment - modification of quantum mechanics at finite temperatures; we call it (ℏ,k)-dynamics ($ \hbar kD$). This approach allows us in a new manner to calculate some important macroparameters and to modify standard thermodynamics. We create an effective apparatus for features description of nearly perfect fluids in various mediums. As an essentially new model of an object environment we suppose a quantum heat bath and its properties, including cases of cold and warm vacuums, are studied. We describe the thermal equilibrium state in place of the traditional density operator in term of a wave function the amplitude and phase of which have temperature dependence. We introduce a new generative operator, Schroedingerian, or stochastic action operator, and show its fundamental role in the microdescription. We demonstrate that a new macroparameter, namely the effective action, can be obtained through averaging of the Schroedingerian over the temperature dependent wave function. It is established that such different parameters as internal energy, effective temperature, and effective entropy and their fluctuations can be expressed through a single quantity - the effective action.
We propose an approach that makes it possible to narrow the gap between the macro- and micro-descriptions of nature (i.e., between thermodynamics and quantum mechanics). This approach is based on introducing the quantum-thermostat model in the form of cold and thermal vacuums. In this case we start from our previously developed microdescription in the form of ( ħ, k ) dynamics instead of the standard quantum mechanics. It is based on using the complex wave function of vacuum. We emphasize the universal role of the stochastic environmental influence in the appearance of correlations between the fluctuations of conjugate parameters on micro- and macrolevels at any temperatures.
To understand in detail the relation between unitary quantum theory that describes our world at the microscopic scale and thermodynamics, which was long believed only to apply to macroscopic objects, is one of the most interesting and long-standing problems in physics. Recently, this problem has received renewed attention, in particular from the community of quantum information theory, but also from the field of statistical mechanics, inspired from stochastic thermodynamics. These results suggest that thermodynamics is also relevant for individual quantum systems, provided that they can be brought into contact with thermal baths. In this thesis, I use recently developed tools to provide new results both on fundamental questions, but also on questions which are of practical relevance for potential miniaturized thermal machines. In terms of fundamental questions, the results in this thesis contribute to understanding how the basic laws of thermodynamics and statistical mechanics can be understood directly from unitary quantum mechanics. In particular, I discuss and answer the following questions: i) How can we quantify the third law of thermodynamics using information theoretic methods? ii) How can we quantify the "thermodynamic value" of a state-transition in quantum systems? iii) How can we axiomatically characterize the non-equilibrium free energy and relative entropy? iv) How can we justify statistical ensembles from an operational perspective, without having to introduce either some probability measures or an information theoretic entropy measure? v) How can we understand the equilibration of closed quantum systems, how long does it take and how difficult is it to avoid? In the second part of the thesis I discuss in detail how experimental restrictions, which become important at the quantum scale, influence the ultimate thermodynamic bounds for thermal machines. In particular, the results in this thesis provide thermodynamic bounds on work-extraction and efficiencies of thermal machines in situations where 1.) an experimenter only has limited field strengths available, 2.) an experimenter cannot control the interactions between particles, but external fields arbitrarily well, and 3.) situations in which a small quantum system can only be strongly coupled to heat baths. These bounds are tight and I provide explicit examples illustrating the different behaviours. Finally, I come back to a classic problem in statistical physics: The emergence of spontaneous symmetry breaking. Here, I provide general and rigorous new results that show how symmetry-breaking stationary states emerge from fluctuations in order parameters in dissipative lattice models.
For a small system at a low temperature, thermal fluctuation and quantum effect play important roles in quantum thermodynamics. Starting from micro-canonical ensemble, we generalize the Boltzmann–Gibbs statistical factor from infinite to finite systems, no matter the interactions between particles are considered or not. This generalized factor, similar to Tsallis’s q-form as a power-law distribution, has the restriction of finite energy spectrum and includes the nonextensivities of the small systems. We derive the exact expression for distribution of average particle numbers in the interacting classical and quantum nonextensive systems within a generalized canonical ensemble. This expression in the almost independent or elementary excitation quantum finite systems is similar to the corresponding ones obtained from the conventional grand-canonical ensemble. In the reconstruction for the statistical theory of the small systems, we present the entropy of the equilibrium systems and equation of total thermal energy. When we investigate the thermodynamics for the interacting nonextensive systems, we obtain the system–bath heat exchange and “uncompensated heat” which are in the thermodynamical level and independent on the detail of the system–bath coupling. For ideal finite systems, with different traps and boundary conditions, we calculate some thermodynamic quantities, such as the specific heat, entropy, and equation of state, etc. Particularly at low temperatures for the small systems, we predict some novel behaviors in the quantum thermodynamics, including internal entropy production, heat exchanges between the system and its surroundings and finite-size effects on the free energy.
A definition of nonequilibrium free energy Fs is proposed for dynamical Gaussian quantum open systems strongly coupled to a heat bath and the formal relation with the generating functional, the coarse-grained effective action and the influence action is indicated. For Gaussian open quantum systems exemplified by the quantum Brownian motion model studied here, a time-varying effective temperature can be introduced in a natural way, and, with it, the nonequilibrium free energy Fs, von Neumann entropy SvN and internal energy Us of the reduced system (S) can be defined accordingly. In contrast to the nonequilibrium free energy found in the literature which references the bath temperature, the nonequilibrium thermodynamic functions we find here obey the familiar relation ${\mathcal{F}}_{\mathrm{s}}(t)={\mathcal{U}}_{\mathrm{s}}(t)\ensuremath{-}{T}_{\mathrm{EFF}}(t){\mathcal{S}}_{vN}(t)$ at any and all moments of time in the system's fully nonequilibrium evolution history. After the system equilibrates they coincide, in the weak coupling limit, with their counterparts in conventional equilibrium thermodynamics. Since the effective temperature captures both the state of the system and its interaction with the bath, upon the system's equilibration, it approaches a value slightly higher than the initial bath temperature. Notably, it remains nonzero for a zero-temperature bath, signaling the existence of system-bath entanglement. Reasonably, at high bath temperatures and under ultraweak couplings, it becomes indistinguishable from the bath temperature. The nonequilibrium thermodynamic functions and relations discovered here for dynamical Gaussian quantum systems should open up useful pathways toward establishing meaningful theories of nonequilibrium quantum thermodynamics.
An exact stochastic model for the thermalization of quantum states is proposed. The model has various physically appealing properties. The dynamics are characterized by an underlying Schrödinger evolution, together with a nonlinear term driving the system toward an asymptotic equilibrium state and a stochastic term reflecting fluctuations. There are two free parameters, one of which can be identified with the heat bath temperature, while the other determines the characteristic time scale for thermalization. Exact expressions are derived for the evolutionary dynamics of the system energy, the system entropy, and the associated density operator.