Standard Thermodynamics Research Articles

Energy-temperature uncertainty relation in quantum thermodynamics

It is known that temperature estimates of macroscopic systems in equilibrium are most precise when their energy fluctuations are large. However, for nanoscale systems deviations from standard thermodynamics arise due to their interactions with the environment. Here we include such interactions and, using quantum estimation theory, derive a generalised thermodynamic uncertainty relation valid for classical and quantum systems at all coupling strengths. We show that the non-commutativity between the system’s state and its effective energy operator gives rise to quantum fluctuations that increase the temperature uncertainty. Surprisingly, these additional fluctuations are described by the average Wigner-Yanase-Dyson skew information. We demonstrate that the temperature’s signal-to-noise ratio is constrained by the heat capacity plus a dissipative term arising from the non-negligible interactions. These findings shed light on the interplay between classical and non-classical fluctuations in quantum thermodynamics and will inform the design of optimal nanoscale thermometers.

Theoretical investigation on H abstraction reaction mechanisms and rate constants of sevoflurane with the OH radical

The H abstraction reaction mechanism for sevoflurane with an ·OH radical was investigated theoretically using dual levels B3LYP/6-311++G(d, p)//QCISD(T)/6-311G(d, p). Thermochemistry properties at 298.15–2000 K were analyzed with the standard statistical thermodynamics method. Three pathways P(1), P(2) and P(3) were found and corresponded to the H13, H14 and H15 abstractions reactions with the Gibbs free barriers of 54.86, 55.05 and 54.86 kJ mol−1, respectively. The corresponding rate constants for three pathways over a wide temperature range of 298.15–2000 K were calculated and the results are in good agreement with the experimental data.

Fluctuations in single-shot ε -deterministic work extraction

There has been an increasing interest in the quantification of nearly deterministic work extraction from a finite number of copies of microscopic particles in finite time. This paradigm, so called single-shot epsilon-deterministic work extraction, considers processes with small failure probabilities. However, the resulting fluctuations in the extracted work entailed by this failure probability have not been studied before. In the standard thermodynamics paradigm fluctuation theorems are powerful tools to study fluctuating quantities. Given that standard fluctuation theorems are inadequate for a single-shot scenario, here we formulate and prove a fluctuation relation specific to the single-shot epsilon-deterministic work extraction to bridge this gap. Our results are general in the sense that we allow the system to be in contact with the heat bath at all times. As a corollary of our theorem we derive the known bounds on the epsilon-deterministic work.

Bounds on large extra dimensions from the Generalized Uncertainty Principle

The Generalized Uncertainty Principle (GUP) implies the existence of a physical minimum length scale [Formula: see text]. In this scenario, black holes must have a radius larger than [Formula: see text]. They are hotter and evaporate faster than in standard Hawking thermodynamics. We study the effects of the GUP on black hole production and decay at the LHC in models with large extra dimensions. Lower bounds on the fundamental Planck scale and the minimum black hole mass at formation are determined from black hole production cross-section limits by the CMS Collaboration. The existence of a minimum length generally decreases the lower bounds on the fundamental Planck scale obtained in the absence of a minimum length.

Dynamics of charged bulk viscous collapsing cylindrical source with heat flux

In this paper, we have explored the effects of dissipation on the dynamics of charged bulk viscous collapsing cylindrical source which allows the out-flow of heat flux in the form of radiations. The Misner–Sharp formalism has been implemented to drive the dynamical equation in terms of proper time and radial derivatives. We have investigated the effects of charge and bulk viscosity on the dynamics of collapsing cylinder. To determine the effects of radial heat flux, we have formulated the heat transport equations in the context of Müller–Israel–Stewart theory by assuming that thermodynamics viscous/heat coupling coefficients can be neglected within some approximations. In our discussion, we have introduced the viscosity by the standard (non-causal) thermodynamics approach. The dynamical equations have been coupled with the heat transport equation; the consequences of the resulting coupled heat equation have been analyzed in detail.

The micromechanical nature of stresses in triphasic granular media with interfaces

The total stress tensor as the average stress within a triphasic granular medium is formally derived from micromechanics where internal forces associated with the solid phase, the two immiscible fluid phases and the associated three interfaces are explicitly accounted for. It is demonstrated that for rigid solid particles, the contributions of all local solid-fluid surface tensions to the total stress are eventually zero. The present work gives the total stress expression as a function of a solid-phase specific stress tensor and a fluid mixture stress contribution that is related to the material's microstructure. A generally non-spherical fluid mixture stress is obtained in contrast to an averaged hydrostatic fluid pressure usually associated with standard thermodynamics. The tensorial nature of this fluid mixture stress contribution is highlighted through numerical experiments pertaining to an idealized granular material in the pendular regime at low wetting saturations. Numerical simulations providing full access to microstructural information are conducted using the Discrete Element Method (DEM), which describes internal forces using resultant forces that clearly deviate from the distributed nature of internal forces in triphasic granular media, e.g., fluid pressures. Nevertheless, this micro-scale representation is demonstrated to be indeed valid for macro-scale stress description in the pendular regime.

Dynamical quantum phase transitions (Review Article)

During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and thermodynamics in equilibrium. Since the dynamics of a many-body quantum system typically involve many excited eigenstates, with a non-thermal distribution, the time evolution of such a system provides an unique way for investigation of non-equilibrium quantum statistical mechanics. Last decade such new subjects like quantum quenches, thermalization, pre-thermalization, equilibration, generalized Gibbs ensemble, etc. are among the most attractive topics of investigation in modern quantum physics. One of the most interesting themes in the study of dynamics of quantum many-body systems out of equilibrium is connected with the recently proposed important concept of dynamical quantum phase transitions. During the last few years a great progress has been achieved in studying of those singularities in the time dependence of characteristics of quantum mechanical systems, in particular, in understanding how the quantum critical points of equilibrium thermodynamics affect their dynamical properties. Dynamical quantum phase transitions reveal universality, scaling, connection to the topology, and many other interesting features. Here we review the recent achievements of this quickly developing part of low-temperature quantum physics. The study of dynamical quantum phase transitions is especially important in context of their connection to the problem of the modern theory of quantum information, where namely non-equilibrium dynamics of many-body quantum system plays the major role.

A Langevin Canonical Approach to the Study of Quantum Stochastic Resonance in Chiral Molecules

A Langevin canonical framework for a chiral two-level system coupled to a bath of harmonic oscillators is used within a coupling scheme different from the well-known spin-boson model. From this stochastic dynamics, within the Markovian regime and Ohmic friction, some standard quantum thermodynamics functions such as the energy average and heat capacity can be extracted. In particular, special emphasis is put on the so-called quantum stochastic resonance which is a cooperative effect of friction, noise and periodic driving occurring in a bistable system.

Mechanical approach to chemical transport

Nonequilibrium thermodynamics describes the rates of transport phenomena with the aid of various thermodynamic forces, but often the phenomenological transport coefficients are not known, and the description is not easily connected with equilibrium relations. We present a simple and intuitive model to address these issues. Our model is based on Lagrangian dynamics for chemical systems with dissipation, so one may think of the model as physicochemical mechanics. Using one main equation, the model allows a systematic derivation of all transport and equilibrium equations, subject to the limitation that heat generated or absorbed in the system must be small for the model to be valid. A table with all major examples of transport and equilibrium processes described using physicochemical mechanics is given. In equilibrium, physicochemical mechanics reduces to standard thermodynamics and the Gibbs-Duhem relation, and we show that the First and Second Laws of thermodynamics are satisfied for our system plus bath model. Out of equilibrium, our model provides relationships between transport coefficients and describes system evolution in the presence of several simultaneous external fields. The model also leads to an extension of the Onsager-Casimir reciprocal relations for properties simultaneously transported by many components.

Design of Compressor less Solar Powered Refrigerator

The thermoelectric effect has been proven as a source of cooling and small power generation as defined by the Peltier-Seebeck effect. Thermoelectric modules, optimized by semiconductors, have been used for temperature regulation by operating as a heat pump to maintain computing devices and integrated circuits at optimum temperatures for improved processing efficiency. Thermoelectric modules have also been used to capture microwatt electrical power from personal computing and other small scale devices by way of utilizing the waste heat rejected through its heat sink. In modern data centers and server farms, water cooling of electronics has been widely adapted as a more efficient cooling method than standard air conditioning and ventilation systems due to its vastly larger thermal capacity. However, even high density electronics cabinets and processing units are low level heat applications unfit for waste heat recovery by standard thermodynamics cycles and heat pumps. When applying the thermoelectric effect to the temperature difference between the heat source of the processing electronics and the heat sink of a water cooling system, potential exists for practical and economic energy recovery. This study demonstrates the feasibility of waste energy recovery from high power density electronics in data centers and server farms by way of the practical and economic application of thermoelectricity. An overview of thermoelectricity and the thermoelectric effect is given, including a review of semiconductor materials and electronics cabinet cooling techniques. This report describes an investigation into the efficiency of applying thermoelectricity to low temperature waste heat situations. Conclusions are presented concerning the effectiveness of this application towards waste heat utilization for power recovery.

Quantum thermodynamics

Quantum thermodynamics is an emerging research field aiming to extend standard thermodynamics and non-equilibrium statistical physics to ensembles of sizes well below the thermodynamic limit, in non-equilibrium situations and with the full inclusion of quantum effects. Fuelled by experimental advances and the potential of future nanoscale applications, this research effort is pursued by scientists with different backgrounds, including statistical physics, many-body theory, mesoscopic physics and quantum information theory, who bring various tools and methods to the field. A multitude of theoretical questions are being addressed ranging from issues of thermalisation of quantum systems and various definitions of ‘work’ to the efficiency and power of quantum engines. This overview provides a perspective on a selection of these current trends accessible to postgraduate students and researchers alike.

Homogenization of intergranular fracture towards a transient gradient damage model

This paper focuses on the intergranular fracture of polycrystalline materials, where a detailed model at the meso-scale is translated onto the macro-level through a proposed homogenization theory. The bottom-up strategy involves the introduction of an additional macro-kinematic field to characterize the average displacement jump within the unit cell. Together with the standard macro-strain field, the underlying processes are propagated onto the macro-scale by imposing the equivalence of power and energy at the two scales. The set of macro-governing equations and constitutive relations are next extracted naturally as per standard thermodynamics procedure. The resulting homogenized microforce balance recovers the so-called ‘implicit’ gradient expression with a transient nonlocal interaction. The homogenized gradient damage model is shown to fully regularize the softening behavior, i.e. the structural response is made mesh-independent, with the damage strain correctly localizing into a macroscopic crack, hence resolving the spurious damage growth observed in many conventional gradient damage models. Furthermore, the predictive capability of the homogenized model is demonstrated by benchmarking its solutions against reference meso-solutions, where a good match is obtained with minimal calibrations, for two different grain sizes.

Measuring “hotness”: Should the sensor’s readings for rapid temperature changes be named “tempericity”?

Expansion of the meaning of “temperature” into “hotness” is discussed and analyzed, with the goal of encompassing its two aspects: the physical quantity (thermodynamic, under equilibrium) and the operational quantity (experimentally observed under off-equilibrium circumstances by the sensor’s thermoscopic reading). For standard TA methods of controlled heating and/or cooling, the standard thermodynamics applies well, but when the temperature changes very rapidly (methods of sample quenching), the customary thermodynamics is inadequate. Notwithstanding the special microchip techniques developed specifically to study rapidly changing-temperature systems, which are capable of handling cooling rates as fast as million Kelvin’s per second, the accuracy of the produced temperature data remains questionable. For such off-equilibrium, poorly defined temperature-measuring systems, a new term “tempericity” is proposed.

Thermodynamic optimization of a Penrose process: An engineers’ approach to black hole thermodynamics

In this work we present a new view on the thermodynamics of black holes introducing effects of irreversibility by employing thermodynamic optimization and finite-time thermodynamics. These questions are of importance both in physics and in engineering, combining standard thermodynamics with optimal control theory in order to find optimal protocols and bounds for realistic processes without assuming anything about the microphysics involved. We find general bounds on the maximum work and the efficiency of thermodynamic processes involving black holes that can be derived exclusively from the knowledge of thermodynamic relations at equilibrium. Since these new bounds consider the finite duration of the processes, they are more realistic and stringent than their reversible counterparts. To illustrate our arguments, we consider in detail the thermodynamic optimization of a Penrose process, i.e. the problem of finding the least dissipative process extracting all the angular momentum from a Kerr black hole in finite time. We discuss the relevance of our results for real astrophysical phenomena, for the comparison with laboratory black holes analogues and for other theoretical aspects of black hole thermodynamics.

Equation of state for a trapped quantum gas: remnant of zero-point energy effects

The study of the thermodynamic properties of trapped gases has attracted great attention during the last few years and can be used as a tool to characterize such clouds in the presence of other phenomena. Here, we obtain an equation of state for a harmonically trapped Bose–Einstein condensate taking the limit of by means of global themodynamic variables. These variables allow us to explore limits in which the standard thermodynamics are not defined. Our results are taken in the high density limit, and the extrapolation for is done later. Even in this situation, we qualitatively observe the well known existence of a zero-point energy for harmonic potentials in which the determination of conjugated variables is limited by the quantum nature of the system.

Kinetics investigation of the hydrogen abstraction reaction between CH3SS and CN radicals.

The reaction mechanisms and rates for the H abstraction reactions between CH3SS and CN radicals in the gas phase were investigated with density functional theory (DFT) methods. The geometries, harmonic vibrational frequencies, and energies of all stationary points were obtained at B3PW91/6-311G(d,p) level of theory. Relationships between the reactants, intermediates, transition states and products were confirmed, with the frequency and the intrinsic reaction coordinate (IRC) analysis at the same theoretical level. High accurate energy information was provided by the G3(MP2) method combined with the standard statistical thermodynamics. Gibbs free energies at 298.15 K for all of the reaction steps were reported, and were used to describe the profile diagrams of the potential energy surface. The rate constants were evaluated with both the classical transition state theory and the canonical variational transition state theory, in which the small-curvature tunneling correction was included. A total number of 9 intermediates (IMs) and 17 transition states (TSs) were obtained. It is shown that IM1 is the most stable intermediate by the largest energy release, and the channel of CH3SS + CN → IM3 → TS10 → P1(CH2SS + HCN) is the dominant reaction with the lowest energy barrier of 144.7 kJ mol(-1). The fitted Arrhenius expressions of the calculated CVT/SCT rate constants for the rate-determining step of the favorable channel is k =7.73 × 10(6) T (1.40)exp(-14,423.8/T) s(-1) in the temperature range of 200-2000 K. The apparent activation energy E a(app.) for the main channel is -102.5 kJ mol(-1), which is comparable with the G3(MP2) energy barrier of -91.8 kJ mol(-1) of TS10 (relative to the reactants).

Entropy production in a heat conduction problem

Heat conduction along an isolated bar placed between two reservoirs at different temperatures is studied. The entropy production is considered in detail with two different approaches. In the first one, the whole system (the bar and the two reservoirs) is analysed in the steady state with the help of standard thermodynamics. In the second one, the bar is divided into n cells and a simple finite difference method is used to evaluate the time evolution of the entropy production. This approach is useful because the transient behaviour can be studied. In this way, it is shown a simple example of a non-equilibrium system where the entropy production (even its transient behaviour) can be evaluated with tools at hand of a motivated undergraduate.

Statistical mechanics of holonomic systems as a Brownian motion on smooth manifolds

The statistical mechanics of arbitrary holonomic scleronomous systems subjected to arbitrary external forces is described by specializing the Lagrange and Hamilton equations of motion to those of the Brownian motion on a manifold. In this context, the Klein‐Kramers and Smoluchowski equations are derived in covariant form, and it is demonstrated that these equations have equilibrium solutions corresponding to the Gibbs distribution, in agreement with standard thermodynamics. At last, the Langevin dynamics corresponding to the Smoluchowski limit is found to exactly correspond to the Brownian motion on a smooth manifold. These results find significant applications in the study of several statistical properties of constrained molecular assemblies (e.g. polymers) of interest in chemistry, physics and biology.

Standard Model thermodynamics across the electroweak crossover

Even though the Standard Model with a Higgs mass mH = 125GeV possesses no bulk phase transition, its thermodynamics still experiences a “soft point” at temperatures around T = 160GeV, with a deviation from ideal gas thermodynamics. Such a deviation may have an effect on precision computations of weakly interacting dark matter relic abundances if their mass is in the few TeV range, or on leptogenesis scenarios operating in this temperature range. By making use of results from lattice simulations based on a dimensionally reduced effective field theory, we estimate the relevant thermodynamic functions across the crossover. The results are tabulated in a numerical form permitting for their insertion as a background equation of state into cosmological particle production/decoupling codes. We find that Higgs dynamics induces a non-trivial “structure” visible e.g. in the heat capacity, but that in general the largest radiative corrections originate from QCD effects, reducing the energy density by a couple of percent from the free value even at T > 160GeV.

Consistent thermodynamic framework for interacting particles by neglecting thermal noise

An effective temperature θ, conjugated to a generalized entropy s(q), was introduced recently for a system of interacting particles. Since θ presents values much higher than those of typical room temperatures T≪θ, the thermal noise can be neglected (T/θ≃0) in these systems. Moreover, the consistency of this definition, as well as of a form analogous to the first law of thermodynamics, du=θds(q)+δW, were verified lately by means of a Carnot cycle, whose efficiency was shown to present the usual form, η=1-(θ(2)/θ(1)). Herein we explore further the heat contribution δQ=θds(q) by proposing a way for a heat exchange between two such systems, as well as its associated thermal equilibrium. As a consequence, the zeroth principle is also established. Moreover, we consolidate the first-law proposal by following the usual procedure for obtaining different potentials, i.e., applying Legendre transformations for distinct pairs of independent variables. From these potentials we derive the equation of state, Maxwell relations, and define response functions. All results presented are shown to be consistent with those of standard thermodynamics for T>0.