Schrödinger uncertainty relation for a quantum oscillator in a thermostat

Sukhanov, A. D.

doi:10.1007/s11232-006-0106-5

Cited by 9 publications

(20 citation statements)

References 8 publications

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“…which coincides with expressions (15) or (26) for the effective entropy S * in the QGEST. Using expression (35), we can calculate the effective temperature T * = (dS * /dE * ) −1 and other macroparameters related to the effective entropy S * .…”

Section: Effective Entropy and The Effective Action In Thermal Coheresupporting

confidence: 78%

“…Standard von Neumann expression (37) for the entropy accepted in QESM turns out to be semiclassical and is therefore inadequate for use over the entire temperature range. At the same time, expression (35) following from definition (34) in our proposed TFD version and expressions (15) and (26) in the QGEST are in agreement, and we can use them to determine the effective entropy S * by independent methods adequately accounting for both types of stochastic actions at any temperature.…”

Section: Effective Action and Effective Entropy In Quantum Equilibriumentioning

confidence: 63%

“…In this case, we start from our previously proposed TFD version [25], [26], which is different from the initial version [23], [24]. It was shown in [25], [26] that in the microdescription, the thermal equilibrium state of the quantum oscillator has the meaning of a correlated (thermal) coherent state, which can be described using a temperature-dependent complex wave function. It has the Gaussian form in the coordinate and momentum representations.…”

Section: Effective Entropy and The Effective Action In Thermal Coherementioning

confidence: 99%

“…The coordinate-momentum uncertainty relation in Schrödinger form for the quantum oscillator (for averaging over wave function (31)) is saturated in our TFD version, i.e., it acquires the form of the equality [26] (UP) 2 ≡ (δp) 2 · (δq) 2 = …”

Section: Effective Entropy and The Effective Action In Thermal Coherementioning

confidence: 99%

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A quantum generalization of equilibrium statistical thermodynamics: Effective macroparameters

Sukhanov

2008

Theor Math Phys

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We propose a generalization of statistical thermodynamics in which quantum effects are taken into account on the macrolevel without explicitly using the operator formalism while traditional relations between the macroparameters are preserved. In a generalized thermostat model, thermal equilibrium is characterized by an effective temperature bounded from below. We introduce fundamental theoretical macroparameters: the effective entropy and the effective action. Because the effective entropy is nonzero at low temperatures, we can write the third law of thermodynamics in the form postulated by Nernst. The effective action at any temperature coincides with the product of standard deviations of the coordinate and momentum in the Heisenberg uncertainty relation and is therefore bounded from below. We establish that the ratio of the effective action to the effective entropy in the low-temperature limit is determined by a holistic stochasticaction constant depending on the Planck and Boltzmann constants. We show that the same results can be obtained in the framework of a modified version of thermofield dynamics in which the quantum oscillator is described by a temperature-dependent complex macroscopic wave function. We study the discrepancy between the behavior of the action-to-entropy ratio in the low-temperature limit in our proposed theory and that in quantum equilibrium statistical mechanics, which can be verified experimentally.

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Section: Effective Entropy and The Effective Action In Thermal Coheresupporting

confidence: 78%

Section: Effective Action and Effective Entropy In Quantum Equilibriumentioning

confidence: 63%

Section: Effective Entropy and The Effective Action In Thermal Coherementioning

confidence: 99%

Section: Effective Entropy and The Effective Action In Thermal Coherementioning

confidence: 99%

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A quantum generalization of equilibrium statistical thermodynamics: Effective macroparameters

Sukhanov

2008

Theor Math Phys

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“…In this paper, which is a continuation of [13], where we introduced the original notions of kD, we develop this theory further as a microdescription of an object under thermal equilibrium conditions. It is based on a new microparameter, namely, the stochastic action operator.…”

Section: Possible Approaches To a Consistent Quantum-thermal Descriptmentioning

confidence: 99%

Toward a quantum generalization of equilibrium statistical thermodynamics: ħ-k Dynamics

Sukhanov

Golubeva

2009

Theor Math Phys

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We show that the quantum statistical mechanics (QSM ) describing the quantum and thermal properties of objects only has the sense of a particular semiclassical approximation. We propose a more general microdescription than in QSM of objects in a thermal bath with the vacuum explicitly taken into account; we call it -k dynamics. We construct a qualitatively new model of the object environment, namely, a quantum thermal bath. We study its properties including the cases of a "cold" and a "thermal" vacuum. We introduce the stochastic action operator and show its fundamental role in the microdescription. We establish that the corresponding macroparameter, the effective action, plays just as significant a role in the macrodescription. The most important effective macroparameters of equilibrium quantum statistical thermodynamics-internal energy, temperature, and entropy-are expressed in terms of this macroparameter. Keywords:-k dynamics, quantum thermal bath, cold vacuum, thermal vacuum, stochastic action operator, effective action, quantum-thermal entropy Possible approaches to a consistent quantum-thermal description of natural objectsThe conviction that equilibrium quantum statistical mechanics (QSM) not only is an adequate description of microobjects in a thermal bath but also forms a basis for the corresponding macrodescription has predominated for a fairly long time. In other words, it is assumed that QSM allows obtaining thermodynamic macroparameters from the microdescription and establishing observable interrelations between them (thermodynamic laws, equations of state, etc.) [1]. At the same time, it is well known that there exist such macroparameters, temperature for example, whose analogues have not yet been studied on the microlevel. This leads to introducing the idea of the independence and equality of the micro-and macrodescriptions of nature with a certain interrelation between them [2], [3].We briefly analyze already revealed elements of the limitations of equilibrium QSM as a theory claiming to consistently describe all quantum and thermal phenomena. As is well known, QSM is based on the notion of the density matrix (operator), which in the energy representation has the form of the Gibbs-von Neumann quantum canonical distribution,where ε n is the spectrum of the object energy, F is the free energy determined by the normalization condition, and Θ is the inverse modulus of the distribution. It has the meaning of the Lagrange multiplier in the derivation of distribution (1) from the maximum entropy principle under thermal equilibrium conditions [4].

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Thermodynamic and relativistic uncertainty relations

Artamonov

Plotnikov

2017

J. Phys.: Conf. Ser.

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Schrödinger uncertainty relation for a quantum oscillator in a thermostat

Cited by 9 publications

References 8 publications

A quantum generalization of equilibrium statistical thermodynamics: Effective macroparameters

A quantum generalization of equilibrium statistical thermodynamics: Effective macroparameters

Toward a quantum generalization of equilibrium statistical thermodynamics: ħ-k Dynamics

Thermodynamic and relativistic uncertainty relations

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