Thermodynamics for Finite-Size and Time-Dependent Behavior: Small Systems, Fluctuations, Correlations, and Internal Heterogeneity

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (15 November 2022) | Viewed by 15516

Special Issue Editor

Department of Physics, Arizona State University, Tempe, AZ, USA
Interests: nanothermodynamics; non-equilibrium thermodynamics; fluctuation theorems

Special Issue Information

Dear Colleagues,

Standard thermodynamics was originally developed to describe the thermal properties of large systems with slow cycles, such as steam engines and power plants. Recently, progress has been made to extend the laws of thermodynamics to small systems and short times, thereby allowing theoretical studies to include conservation of energy and maximum entropy for fast fluctuations on length scales of nanometers. Here we seek to bring together various views on how best to adapt standard thermodynamics to accurately describe finite-size and time-dependent behavior. A crucial consideration is how nanoscale effects that arise in thermodynamics may influence standard statistical mechanics. Applications include the study of complex biological molecules, living systems, nanofabricated devices, and symmetry in nanostructured materials. Fundamental interest comes from thermal heterogeneity and statistical symmetry that occur inside bulk systems. Additional interest comes from studying temporal asymmetry in non-equilibrium thermodynamics.

Submit your paper and select the Journal “Symmetry” and the Special Issue “Thermodynamics for Finite-Size and Time-Dependent Behavior: Small Systems, Fluctuations, Correlations, and Internal Heterogeneity” via: MDPI submission system. Our papers will be published on a rolling basis and we will be pleased to receive your submission once you have finished it.

Prof. Dr. Ralph V. Chamberlin
Guest Editor

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Keywords

  • nanothermodynamics
  • stochastic thermodynamics
  • fluctuation theorems
  • non-Gaussian fluctuations
  • active baths
  • maximum entropy
  • information theory
  • non-equilibrium thermodynamics

Published Papers (6 papers)

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Research

16 pages, 13873 KiB  
Article
Experimental Study on the Influence of Gravitational Tilt Angle on the Spatio-Temporal Evolution of Solutocapillary Convection
by Shuo Yang, Daocheng Qin, Yupeng Zhang, Lin Xu, Yudong Fu, Jie Cui and Honggang Pan
Symmetry 2022, 14(12), 2485; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14122485 - 23 Nov 2022
Cited by 4 | Viewed by 862
Abstract
This paper investigated the influence of surface internal energy instability caused by the gravitational tilt angle on solutocapillary convection. The results showed that the spatio-temporal evolution of solutocapillary convection in a non-axisymmetric liquid bridge was divided into three stages under different gravitational tilt [...] Read more.
This paper investigated the influence of surface internal energy instability caused by the gravitational tilt angle on solutocapillary convection. The results showed that the spatio-temporal evolution of solutocapillary convection in a non-axisymmetric liquid bridge was divided into three stages under different gravitational tilt angles, “the initiating stage near the upper corner”, “development to the intermediate height”, and “shrinking toward the bottom corner”. The non-equilibrium of the left or right interface curvature caused by internal energy instability promotes the distortion of the cell flow structure. The concentration gradient on the far-earth side increases first, due to the gravitational tilt angle. With the increasing gravitational tilt angle, the lateral extension of the cell flow is inhibited. The transverse/longitudinal velocity components are suppressed; however, the velocity gradient near the boundary is increased, and the uniformity of the velocity distribution in the center of the liquid bridge is improved. The axial component of the Bond number decreases in a small range (Bo′ = 1→0.98) with the internal energy instability, however, which has a significant effect on surface flow. Therefore, in the initiation and development stages of solutocapillary convection, the decay rate of the Marangoni number respectively decreases and increases with the increasing Bond number. The axial component of the Bond number decreases in a small range with the internal energy instability, which has a significant effect on the solute Marangoni number (Mac). In the initiation stage of solutocapillary convection, the decay rate of the Mac decreases with the increasing Bond number. Its change law is the opposite in the development stage of solutocapillary convection. Full article
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25 pages, 3394 KiB  
Article
An Ising Model for Supercooled Liquids and the Glass Transition
by Ralph V. Chamberlin
Symmetry 2022, 14(10), 2211; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14102211 - 20 Oct 2022
Cited by 1 | Viewed by 1307
Abstract
We describe the behavior of an Ising model with orthogonal dynamics, where changes in energy and changes in alignment never occur during the same Monte Carlo (MC) step. This orthogonal Ising model (OIM) allows conservation of energy and conservation of (angular) momentum to [...] Read more.
We describe the behavior of an Ising model with orthogonal dynamics, where changes in energy and changes in alignment never occur during the same Monte Carlo (MC) step. This orthogonal Ising model (OIM) allows conservation of energy and conservation of (angular) momentum to proceed independently, on their own preferred time scales. The OIM also includes a third type of MC step that makes or breaks the interaction between neighboring spins, facilitating an equilibrium distribution of bond energies. MC simulations of the OIM mimic more than twenty distinctive characteristics that are commonly found above and below the glass temperature, Tg. Examples include a specific heat that has hysteresis around Tg, out-of-phase (loss) response that exhibits primary (α) and secondary (β) peaks, super-Arrhenius T dependence for the α-response time (τα), and fragilities that increase with increasing system size (N). Mean-field theory for energy fluctuations in the OIM yields a critical temperature (Tc) and a novel expression for the super-Arrhenius divergence as TTc: ln(τα)~1/(1Tc/T)2. Because this divergence is reminiscent of the Vogel-Fulcher-Tammann (VFT) law squared, we call it the “VFT2 law”. A modified Stickel plot, which linearizes the VFT2 law, shows that at high T where mean-field theory should apply, only the VFT2 law gives qualitatively consistent agreement with measurements of τα (from the literature) on five glass-forming liquids. Such agreement with the OIM suggests that several basic features govern supercooled liquids. The freezing of a liquid into a glass involves an underlying 2nd-order transition that is broadened by finite-size effects. The VFT2 law for τα comes from energy fluctuations that enhance the pathways through an entropy bottleneck, not activation over an energy barrier. Values of τα vary exponentially with inverse N, consistent with the distribution of relaxation times deduced from measurements of α response. System sizes found via the T dependence of τα from simulations and measurements are similar to sizes of independently relaxing regions (IRR) measured by nuclear magnetic resonance (NMR) for simple-molecule glass-forming liquids. The OIM elucidates the key ingredients needed to interpret the thermal and dynamic properties of amorphous materials, while providing a broad foundation for more-detailed models of liquid-glass behavior. Full article
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7 pages, 678 KiB  
Article
Crossover in Extended Newtonian Gravity Emerging from Thermodynamics
by Sumiyoshi Abe and Peter Ván
Symmetry 2022, 14(5), 1048; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14051048 - 20 May 2022
Cited by 2 | Viewed by 1238
Abstract
Recently, it has been discovered that a scalar field coupled to a fluid and allowed to be a thermodynamic variable in consistency with the second law of thermodynamics is only of gravity, and, accordingly, the emergence of extended Newtonian gravity has been predicted. [...] Read more.
Recently, it has been discovered that a scalar field coupled to a fluid and allowed to be a thermodynamic variable in consistency with the second law of thermodynamics is only of gravity, and, accordingly, the emergence of extended Newtonian gravity has been predicted. The resulting field equation for the potential of this emergent force is nonlinear and admits the logarithmic potential as a singular solution, suggesting its relevance to the dark matter conundrum. Here, a general analysis of the nonlinear field equation is performed. It is found that the emergent force field exhibits an unsharp crossover between the 1/r and 1/r2 forces outside the fluid, depending on a spatial scale characteristic of the present theory to be observationally tested in the context of the dark matter conundrum. Then, the action functional is constructed for the potential of the emergent field, and the field energy is shown to be free from an infrared divergence. A comment is also made on the difference of the present theory to MOND (modified Newtonian dynamics). Full article
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8 pages, 250 KiB  
Article
On Nonuniqueness of Quantum Channel for Fixed Input-Output States: Case of Decoherence Channel
by Congjie Ou and Sumiyoshi Abe
Symmetry 2022, 14(2), 214; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14020214 - 22 Jan 2022
Viewed by 1789
Abstract
For a fixed pair of input and output states in the space HA of a system A, a quantum channel, i.e., a linear, completely positive and trace-preserving map, between them is not unique, in general. Here, this point is discussed specifically [...] Read more.
For a fixed pair of input and output states in the space HA of a system A, a quantum channel, i.e., a linear, completely positive and trace-preserving map, between them is not unique, in general. Here, this point is discussed specifically for a decoherence channel, which maps from a pure input state to a completely decoherent state like the thermal state. In particular, decoherence channels of two different types are analyzed: one is unital and the other is not, and both of them can be constructed through reduction of B in the total extended space HAHB, where HB is the space of an ancillary system B that is a replica of A. The nonuniqueness is seen to have its origin in the unitary symmetry in the extended space. It is shown in an example of a two-qubit system how such symmetry is broken in the objective subspace HA due to entanglement between A and B. A comment is made on possible relevance of the present work to nanothermodynamics in view of quantum Darwinism. Full article
15 pages, 1419 KiB  
Article
Quantum Heat Engines with Singular Interactions
by Nathan M. Myers, Jacob McCready and Sebastian Deffner
Symmetry 2021, 13(6), 978; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13060978 - 31 May 2021
Cited by 12 | Viewed by 4908
Abstract
By harnessing quantum phenomena, quantum devices have the potential to outperform their classical counterparts. Here, we examine using wave function symmetry as a resource to enhance the performance of a quantum Otto engine. Previous work has shown that a bosonic working medium can [...] Read more.
By harnessing quantum phenomena, quantum devices have the potential to outperform their classical counterparts. Here, we examine using wave function symmetry as a resource to enhance the performance of a quantum Otto engine. Previous work has shown that a bosonic working medium can yield better performance than a fermionic medium. We expand upon this work by incorporating a singular interaction that allows the effective symmetry to be tuned between the bosonic and fermionic limits. In this framework, the particles can be treated as anyons subject to Haldane’s generalized exclusion statistics. Solving the dynamics analytically using the framework of “statistical anyons”, we explore the interplay between interparticle interactions and wave function symmetry on engine performance. Full article
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19 pages, 645 KiB  
Article
Fluctuation–Dissipation Relations in Active Matter Systems
by Lorenzo Caprini, Andrea Puglisi and Alessandro Sarracino
Symmetry 2021, 13(1), 81; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13010081 - 05 Jan 2021
Cited by 25 | Viewed by 4359
Abstract
We investigate the non-equilibrium character of self-propelled particles through the study of the linear response of the active Ornstein–Uhlenbeck particle (AOUP) model. We express the linear response in terms of correlations computed in the absence of perturbations, proposing a particularly compact and readable [...] Read more.
We investigate the non-equilibrium character of self-propelled particles through the study of the linear response of the active Ornstein–Uhlenbeck particle (AOUP) model. We express the linear response in terms of correlations computed in the absence of perturbations, proposing a particularly compact and readable fluctuation–dissipation relation (FDR): such an expression explicitly separates equilibrium and non-equilibrium contributions due to self-propulsion. As a case study, we consider non-interacting AOUP confined in single-well and double-well potentials. In the former case, we also unveil the effect of dimensionality, studying one-, two-, and three-dimensional dynamics. We show that information about the distance from equilibrium can be deduced from the FDR, putting in evidence the roles of position and velocity variables in the non-equilibrium relaxation. Full article
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