Erratum: The significance of Weinhold’s length [J. Chem. Phys. <b>7</b>
                  <b>3</b>, 1001 (1980)]

Salamon, Peter; Andresen, Bjarne; Gait, P. D.; Berry, R. S.

doi:10.1063/1.440781

Cited by 9 publications

(9 citation statements)

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“…Therefore, reactions of the type nA a mB a lC with B as the desired product will have to be treated differently. In a quantitative description a thermodynamic metric M is introduced, 22,23 consisting of the second derivatives of one of the extensive variables with respect to all the others, e.g. 15 B. Thermodynamic Distance.…”

Section: Discussionmentioning

confidence: 99%

Finite-Time Optimization of Chemical Reactions: nA ⇄ mB

Christian

Andresen

1996

J. Phys. Chem.

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We investigate the optimization of chemical reactions of the type nA a mB in a closed container. The goal is to produce a maximal amount of A or B within a given finite time. The controls are taken to be volume and temperature, restricted to allowed regions in (V, )-space with ) 1/kT. We show that the optimal path is achieved by choosing V and such that, for the current amounts of reaction products N A and N B , the reaction rate f(N B ,N A ,V, ) ) dN B /dt is at all times maximal or minimal. For different combinations of endo/ exothermicity and activation energies switches between extremal values of V and/or may be included in the optimal path. The resulting paths are described qualitatively for general values of n and m, while the reactions 2NH 3 a N 2 + 3H 2 , N 2 O 4 a 2NO 2 , and 2NO 2 a N 2 + 2O 2 are used as concrete examples. It is observed that the optimal and equilibrium paths differ by a constant ∆ ; a possible connection with a constant thermodynamic speed path is discussed.Finite-Time Optimization of Chemical Reactions: nA a mB

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Section: Discussionmentioning

confidence: 99%

Finite-Time Optimization of Chemical Reactions: nA ⇄ mB

Christian

Andresen

1996

J. Phys. Chem.

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“…Eq. ( 38) tells us that it is lower-bounded by a purely geometric quantity which depends on the path, thermodynamic length L. Interestingly, the minimum value of L 2 is attained when the integrand is constant along the path [141,142,146]. These ideas became recently very useful in the study of the slow evolution of driven qubits.…”

Section: Adiabatic Regime and Thermodynamic Lengthmentioning

confidence: 99%

Energy dynamics, heat production and heat-work conversion with qubits: towards the development of quantum machines

Arrachea¹

2022

Preprint

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We present an overview of recent advances in the study of energy dynamics and mechanisms for energy conversion in qubit systems with special focus on realizations in superconducting quantum circuits. We briefly introduce the relevant theoretical framework to analyze heat generation, energy transport and energy conversion in these systems with and without time-dependent driving considering the effect of equilibrium and non-equilibrium environments. We analyze specific problems and mechanisms under current investigation in the context of qubit systems. These include the problem of energy dissipation and possible routes for its control, energy pumping between driving sources and heat pumping between reservoirs, implementation of thermal machines and mechanisms for energy storage. We highlight the underlying fundamental phenomena related to geometrical and topological properties, as well as many-body correlations. We also present an overview of recent experimental activity in this field.

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“…(9) and (18) has both Killing and event horizons [61]. The Killing horizon is a null surface whose null generators are tangent to a Killing field.…”

Section: Conserved and Thermodynamics Quantities Of Rotating Black Brmentioning

confidence: 99%

“…The Weinhold's metric is in terms of the second derivatives of the internal energy with respect to entropy and other extensive variables of a thermodynamic system. By this metric, we can study the properties of the space, such as thermodynamic length [9][10][11], the physical properties of various two-dimensional thermodynamic systems [12][13][14][15], and the associated Riemannian structure [16,17]. The Ruppeiner'metric is a Riemannian metric structure in thermodynamic fluctuation theory, and is defined as the second derivatives of the entropy.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear electrodynamics and thermodynamic geometry of rotating dilaton black branes

2016

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We construct a new class of rotating dilaton solutions in the presence of logarithmic nonlinear electrodynamics. These solutions represent black branes with flat horizon and contain k = [(n − 1)/2] rotation parameters in n-dimensional spacetime where [x] is the integer part of x. We study the causal structure of the spacetime and calculate thermodynamic and conserved quantities and show that these quantities satisfy the first law of thermodynamics on the black brane horizon,Then, we study geometrical approach towards thermodynamics by choosing an appropriate geometrical metric. We show that the singularity of the Ricci scalar coincides exactly with the phase transition points. We observe that our system encounters two types of phase transitions depending on the metric parameters. For the first one the heat capacity is zero and for the second one the heat capacity diverges. In the first kind of phase transition, the brane has a transition from an unstable non-physical to a stable physical state. In the second type of phase transition the brane moves from a stable to an unstable state. Finally, we comment on the dynamical stability of the obtained solutions under perturbations in four dimensions.

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Erratum: The significance of Weinhold’s length [J. Chem. Phys. 7 3, 1001 (1980)]

Cited by 9 publications

References 0 publications

Finite-Time Optimization of Chemical Reactions: nA ⇄ mB

Finite-Time Optimization of Chemical Reactions: nA ⇄ mB

Energy dynamics, heat production and heat-work conversion with qubits: towards the development of quantum machines

Nonlinear electrodynamics and thermodynamic geometry of rotating dilaton black branes

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