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Special Issue "Thermodynamics and Statistical Mechanics of Small Systems"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Mechanics".

Deadline for manuscript submissions: 28 February 2018

Special Issue Editors

Guest Editor
Prof. Dr. Andrea Puglisi

Consiglio Nazionale delle Ricerche (CNR), Istituto dei Sistemi Complessi (ISC), c/o Dipartimento di Fisica, Universita' Sapienza Roma, p.le A. Moro 2, 00185, Roma, Italy
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Interests: granular materials, non-equilibrium statistical mechanics, computational cognitive science
Guest Editor
Dr. Alessandro Sarracino

Istituto dei Sistemi Complessi–CNR and Dipartimento di Fisica, Università “Sapienza”, Piazzale A. Moro 200185 Rome, Italy
Website | E-Mail
Interests: nonequilibrium statistical mechanics; granular systems; anomalous diffusion
Guest Editor
Prof. Dr. Angelo Vulpiani

Dipartimento di Fisica Università degli studi di Roma "La Sapienza", Piazzale A. Moro, 5 00185 Roma, Italy
Website | E-Mail
Interests: dynamical systems; turbulence; statistical mechanics and disordered systems

Special Issue Information

Dear Colleagues,

A challenging frontier in statistical physics concerns systems with a small number N of degrees of freedom, far from the thermodynamic limit: such an interest is motivated by the recent increase of resolution in the observation and in the manipulation of the micro-nano world. The peculiar feature of small systems is the relevance of fluctuations, which cannot be neglected. The study of fluctuations of thermodynamics quantities such as energy or entropy goes back to Einstein, Onsager and Kubo: more recently it has taken an acceleration with the establishing of new results in response theory and in the so-called stochastic thermodynamics. Such a turning point has received a great impulse from the study of systems which are far from thermodynamic equilibrium. Applications of the thermodynamics and statistical mechanics of small systems range from molecular biology to micromechanics, including, among others, models of nanotransport, of Brownian motors and of (living or artificial) self-propelled organisms.

Prof. Dr. Andrea Puglisi
Dr. Alessandro Sarracino
Prof. Dr. Angelo Vulpiani
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1500 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Statistical Mechanics
  • Small Systems
  • Stochastic Thermodynamics
  • Non-Equilibrium Fluctuations
  • Large Deviations

Published Papers (15 papers)

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Research

Open AccessArticle On Work and Heat in Time-Dependent Strong Coupling
Entropy 2017, 19(11), 595; doi:10.3390/e19110595
Received: 18 August 2017 / Revised: 14 September 2017 / Accepted: 28 October 2017 / Published: 7 November 2017
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Abstract
This paper revisits the classical problem of representing a thermal bath interacting with a system as a large collection of harmonic oscillators initially in thermal equilibrium. As is well known, the system then obeys an equation, which in the bulk and in the
[...] Read more.
This paper revisits the classical problem of representing a thermal bath interacting with a system as a large collection of harmonic oscillators initially in thermal equilibrium. As is well known, the system then obeys an equation, which in the bulk and in the suitable limit tends to the Kramers–Langevin equation of physical kinetics. I consider time-dependent system-bath coupling and show that this leads to an additional harmonic force acting on the system. When the coupling is switched on and switched off rapidly, the force has delta-function support at the initial and final time. I further show that the work and heat functionals as recently defined in stochastic thermodynamics at strong coupling contain additional terms depending on the time derivative of the system-bath coupling. I discuss these terms and show that while they can be very large if the system-bath coupling changes quickly, they only give a finite contribution to the work that enters in Jarzynski’s equality. I also discuss that these corrections to standard work and heat functionals provide an explanation for non-standard terms in the change of the von Neumann entropy of a quantum bath interacting with a quantum system found in an earlier contribution (Aurell and Eichhorn, 2015). Full article
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
Open AccessArticle Equilibration in the Nosé–Hoover Isokinetic Ensemble: Effect of Inter-Particle Interactions
Entropy 2017, 19(10), 544; doi:10.3390/e19100544
Received: 19 September 2017 / Revised: 11 October 2017 / Accepted: 11 October 2017 / Published: 14 October 2017
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Abstract
We investigate the stationary and dynamic properties of the celebrated Nosé–Hoover dynamics of many-body interacting Hamiltonian systems, with an emphasis on the effect of inter-particle interactions. To this end, we consider a model system with both short- and long-range interactions. The Nosé–Hoover dynamics
[...] Read more.
We investigate the stationary and dynamic properties of the celebrated Nosé–Hoover dynamics of many-body interacting Hamiltonian systems, with an emphasis on the effect of inter-particle interactions. To this end, we consider a model system with both short- and long-range interactions. The Nosé–Hoover dynamics aim to generate the canonical equilibrium distribution of a system at a desired temperature by employing a set of time-reversible, deterministic equations of motion. A signature of canonical equilibrium is a single-particle momentum distribution that is Gaussian. We find that the equilibrium properties of the system within the Nosé–Hoover dynamics coincides with that within the canonical ensemble. Moreover, starting from out-of-equilibrium initial conditions, the average kinetic energy of the system relaxes to its target value over a size-independent timescale. However, quite surprisingly, our results indicate that under the same conditions and with only long-range interactions present in the system, the momentum distribution relaxes to its Gaussian form in equilibrium over a scale that diverges with the system size. On adding short-range interactions, the relaxation is found to occur over a timescale that has a much weaker dependence on system size. This system-size dependence of the timescale vanishes when only short-range interactions are present in the system. An implication of such an ultra-slow relaxation when only long-range interactions are present in the system is that macroscopic observables other than the average kinetic energy when estimated in the Nosé–Hoover dynamics may take an unusually long time to relax to its canonical equilibrium value. Our work underlines the crucial role that interactions play in deciding the equivalence between Nosé–Hoover and canonical equilibrium. Full article
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
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Open AccessFeature PaperArticle Kovacs-Like Memory Effect in Athermal Systems: Linear Response Analysis
Entropy 2017, 19(10), 539; doi:10.3390/e19100539
Received: 19 September 2017 / Revised: 10 October 2017 / Accepted: 11 October 2017 / Published: 13 October 2017
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Abstract
We analyze the emergence of Kovacs-like memory effects in athermal systems within the linear response regime. This is done by starting from both the master equation for the probability distribution and the equations for the physically-relevant moments. The general results are applied to
[...] Read more.
We analyze the emergence of Kovacs-like memory effects in athermal systems within the linear response regime. This is done by starting from both the master equation for the probability distribution and the equations for the physically-relevant moments. The general results are applied to a general class of models with conserved momentum and non-conserved energy. Our theoretical predictions, obtained within the first Sonine approximation, show an excellent agreement with the numerical results. Furthermore, we prove that the observed non-monotonic relaxation is consistent with the monotonic decay of the non-equilibrium entropy. Full article
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
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Open AccessArticle Hydrodynamics of a Granular Gas in a Heterogeneous Environment
Entropy 2017, 19(10), 536; doi:10.3390/e19100536
Received: 21 August 2017 / Revised: 2 October 2017 / Accepted: 9 October 2017 / Published: 11 October 2017
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Abstract
We analyze the transport properties of a low density ensemble of identical macroscopic particles immersed in an active fluid. The particles are modeled as inelastic hard spheres (granular gas). The non-homogeneous active fluid is modeled by means of a non-uniform stochastic thermostat. The
[...] Read more.
We analyze the transport properties of a low density ensemble of identical macroscopic particles immersed in an active fluid. The particles are modeled as inelastic hard spheres (granular gas). The non-homogeneous active fluid is modeled by means of a non-uniform stochastic thermostat. The theoretical results are validated with a numerical solution of the corresponding the kinetic equation (direct simulation Monte Carlo method). We show a steady flow in the system that is accurately described by Navier-Stokes (NS) hydrodynamics, even for high inelasticity. Surprisingly, we find that the deviations from NS hydrodynamics for this flow are stronger as the inelasticity decreases. The active fluid action is modeled here with a non-uniform fluctuating volume force. This is a relevant result given that hydrodynamics of particles in complex environments, such as biological crowded environments, is still a question under intense debate. Full article
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
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Open AccessArticle Participation Ratio for Constraint-Driven Condensation with Superextensive Mass
Entropy 2017, 19(10), 517; doi:10.3390/e19100517
Received: 30 August 2017 / Revised: 19 September 2017 / Accepted: 22 September 2017 / Published: 26 September 2017
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Abstract
Broadly distributed random variables with a power-law distribution f(m)m-(1+α) are known to generate condensation effects. This means that, when the exponent α lies in a certain interval, the largest variable in a
[...] Read more.
Broadly distributed random variables with a power-law distribution f ( m ) m - ( 1 + α ) are known to generate condensation effects. This means that, when the exponent α lies in a certain interval, the largest variable in a sum of N (independent and identically distributed) terms is for large N of the same order as the sum itself. In particular, when the distribution has infinite mean ( 0 < α < 1 ) one finds unconstrained condensation, whereas for α > 1 constrained condensation takes places fixing the total mass to a large enough value M = i = 1 N m i > M c . In both cases, a standard indicator of the condensation phenomenon is the participation ratio Y k = i m i k / ( i m i ) k ( k > 1 ), which takes a finite value for N when condensation occurs. To better understand the connection between constrained and unconstrained condensation, we study here the situation when the total mass is fixed to a superextensive value M N 1 + δ ( δ > 0 ), hence interpolating between the unconstrained condensation case (where the typical value of the total mass scales as M N 1 / α for α < 1 ) and the extensive constrained mass. In particular we show that for exponents α < 1 a condensate phase for values δ > δ c = 1 / α - 1 is separated from a homogeneous phase at δ < δ c from a transition line, δ = δ c , where a weak condensation phenomenon takes place. We focus on the evaluation of the participation ratio as a generic indicator of condensation, also recalling or presenting results in the standard cases of unconstrained mass and of fixed extensive mass. Full article
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
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Open AccessArticle Far-From-Equilibrium Time Evolution between Two Gamma Distributions
Entropy 2017, 19(10), 511; doi:10.3390/e19100511
Received: 18 August 2017 / Revised: 18 September 2017 / Accepted: 21 September 2017 / Published: 22 September 2017
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Abstract
Many systems in nature and laboratories are far from equilibrium and exhibit significant fluctuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability Distribution Functions (PDFs), especially time-dependent PDFs, becomes essential in
[...] Read more.
Many systems in nature and laboratories are far from equilibrium and exhibit significant fluctuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability Distribution Functions (PDFs), especially time-dependent PDFs, becomes essential in understanding far-from-equilibrium processes. We consider a stochastic logistic model with multiplicative noise, which has gamma distributions as stationary PDFs. We numerically solve the transient relaxation problem and show that as the strength of the stochastic noise increases, the time-dependent PDFs increasingly deviate from gamma distributions. For sufficiently strong noise, a transition occurs whereby the PDF never reaches a stationary state, but instead, forms a peak that becomes ever more narrowly concentrated at the origin. The addition of an arbitrarily small amount of additive noise regularizes these solutions and re-establishes the existence of stationary solutions. In addition to diagnostic quantities such as mean value, standard deviation, skewness and kurtosis, the transitions between different solutions are analysed in terms of entropy and information length, the total number of statistically-distinguishable states that a system passes through in time. Full article
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
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Open AccessArticle Thermodynamics of Small Magnetic Particles
Entropy 2017, 19(9), 499; doi:10.3390/e19090499
Received: 2 August 2017 / Revised: 1 September 2017 / Accepted: 13 September 2017 / Published: 15 September 2017
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Abstract
In the present paper, we discuss the interpretation of some of the results of the thermodynamics in the case of very small systems. Most of the usual statistical physics is done for systems with a huge number of elements in what is called
[...] Read more.
In the present paper, we discuss the interpretation of some of the results of the thermodynamics in the case of very small systems. Most of the usual statistical physics is done for systems with a huge number of elements in what is called the thermodynamic limit, but not all of the approximations done for those conditions can be extended to all properties in the case of objects with less than a thousand elements. The starting point is the Ising model in two dimensions (2D) where an analytic solution exits, which allows validating the numerical techniques used in the present article. From there on, we introduce several variations bearing in mind the small systems such as the nanoscopic or even subnanoscopic particles, which are nowadays produced for several applications. Magnetization is the main property investigated aimed for two singular possible devices. The size of the systems (number of magnetic sites) is decreased so as to appreciate the departure from the results valid in the thermodynamic limit; periodic boundary conditions are eliminated to approach the reality of small particles; 1D, 2D and 3D systems are examined to appreciate the differences established by dimensionality is this small world; upon diluting the lattices, the effect of coordination number (bonding) is also explored; since the 2D Ising model is equivalent to the clock model with q = 2 degrees of freedom, we combine previous results with the supplementary degrees of freedom coming from the variation of q up to q = 20 . Most of the previous results are numeric; however, for the case of a very small system, we obtain the exact partition function to compare with the conclusions coming from our numerical results. Conclusions can be summarized in the following way: the laws of thermodynamics remain the same, but the interpretation of the results, averages and numerical treatments need special care for systems with less than about a thousand constituents, and this might need to be adapted for different properties or devices. Full article
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
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Open AccessArticle A Chain, a Bath, a Sink, and a Wall
Entropy 2017, 19(9), 445; doi:10.3390/e19090445
Received: 22 June 2017 / Revised: 22 August 2017 / Accepted: 24 August 2017 / Published: 25 August 2017
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Abstract
We numerically investigate out-of-equilibrium stationary processes emerging in a Discrete Nonlinear Schrödinger chain in contact with a heat reservoir (a bath) at temperature TL and a pure dissipator (a sink) acting on opposite edges. Long-time molecular-dynamics simulations are performed by evolving the
[...] Read more.
We numerically investigate out-of-equilibrium stationary processes emerging in a Discrete Nonlinear Schrödinger chain in contact with a heat reservoir (a bath) at temperature T L and a pure dissipator (a sink) acting on opposite edges. Long-time molecular-dynamics simulations are performed by evolving the equations of motion within a symplectic integration scheme. Mass and energy are steadily transported through the chain from the heat bath to the sink. We observe two different regimes. For small heat-bath temperatures T L and chemical-potentials, temperature profiles across the chain display a non-monotonous shape, remain remarkably smooth and even enter the region of negative absolute temperatures. For larger temperatures T L , the transport of energy is strongly inhibited by the spontaneous emergence of discrete breathers, which act as a thermal wall. A strongly intermittent energy flux is also observed, due to the irregular birth and death of breathers. The corresponding statistics exhibit the typical signature of rare events of processes with large deviations. In particular, the breather lifetime is found to be ruled by a stretched-exponential law. Full article
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
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Open AccessArticle Parameterization of Coarse-Grained Molecular Interactions through Potential of Mean Force Calculations and Cluster Expansion Techniques
Entropy 2017, 19(8), 395; doi:10.3390/e19080395
Received: 24 May 2017 / Revised: 24 July 2017 / Accepted: 24 July 2017 / Published: 1 August 2017
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Abstract
We present a systematic coarse-graining (CG) strategy for many particle molecular systems based on cluster expansion techniques. We construct a hierarchy of coarse-grained Hamiltonians with interaction potentials consisting of two, three and higher body interactions. In this way, the suggested model becomes computationally
[...] Read more.
We present a systematic coarse-graining (CG) strategy for many particle molecular systems based on cluster expansion techniques. We construct a hierarchy of coarse-grained Hamiltonians with interaction potentials consisting of two, three and higher body interactions. In this way, the suggested model becomes computationally tractable, since no information from long n-body (bulk) simulations is required in order to develop it, while retaining the fluctuations at the coarse-grained level. The accuracy of the derived cluster expansion based on interatomic potentials is examined over a range of various temperatures and densities and compared to direct computation of the pair potential of mean force. The comparison of the coarse-grained simulations is done on the basis of the structural properties, against detailed all-atom data. On the other hand, by construction, the approximate coarse-grained models retain, in principle, the thermodynamic properties of the atomistic model without the need for any further parameter fitting. We give specific examples for methane and ethane molecules in which the coarse-grained variable is the centre of mass of the molecule. We investigate different temperature (T) and density ( ρ ) regimes, and we examine differences between the methane and ethane systems. Results show that the cluster expansion formalism can be used in order to provide accurate effective pair and three-body CG potentials at high T and low ρ regimes. In the liquid regime, the three-body effective CG potentials give a small improvement over the typical pair CG ones; however, in order to get significantly better results, one needs to consider even higher order terms. Full article
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
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Open AccessArticle An Application of Pontryagin’s Principle to Brownian Particle Engineered Equilibration
Entropy 2017, 19(7), 379; doi:10.3390/e19070379
Received: 3 July 2017 / Revised: 19 July 2017 / Accepted: 20 July 2017 / Published: 24 July 2017
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Abstract
We present a stylized model of controlled equilibration of a small system in a fluctuating environment. We derive the optimal control equations steering in finite-time the system between two equilibrium states. The corresponding thermodynamic transition is optimal in the sense that it occurs
[...] Read more.
We present a stylized model of controlled equilibration of a small system in a fluctuating environment. We derive the optimal control equations steering in finite-time the system between two equilibrium states. The corresponding thermodynamic transition is optimal in the sense that it occurs at minimum entropy if the set of admissible controls is restricted by certain bounds on the time derivatives of the protocols. We apply our equations to the engineered equilibration of an optical trap considered in a recent proof of principle experiment. We also analyze an elementary model of nucleation previously considered by Landauer to discuss the thermodynamic cost of one bit of information erasure. We expect our model to be a useful benchmark for experiment design as it exhibits the same integrability properties of well-known models of optimal mass transport by a compressible velocity field. Full article
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
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Open AccessFeature PaperArticle Clausius Relation for Active Particles: What Can We Learn from Fluctuations
Entropy 2017, 19(7), 356; doi:10.3390/e19070356
Received: 12 June 2017 / Revised: 6 July 2017 / Accepted: 12 July 2017 / Published: 13 July 2017
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Abstract
Many kinds of active particles, such as bacteria or active colloids, move in a thermostatted fluid by means of self-propulsion. Energy injected by such a non-equilibrium force is eventually dissipated as heat in the thermostat. Since thermal fluctuations are much faster and weaker
[...] Read more.
Many kinds of active particles, such as bacteria or active colloids, move in a thermostatted fluid by means of self-propulsion. Energy injected by such a non-equilibrium force is eventually dissipated as heat in the thermostat. Since thermal fluctuations are much faster and weaker than self-propulsion forces, they are often neglected, blurring the identification of dissipated heat in theoretical models. For the same reason, some freedom—or arbitrariness—appears when defining entropy production. Recently three different recipes to define heat and entropy production have been proposed for the same model where the role of self-propulsion is played by a Gaussian coloured noise. Here we compare and discuss the relation between such proposals and their physical meaning. One of these proposals takes into account the heat exchanged with a non-equilibrium active bath: such an “active heat” satisfies the original Clausius relation and can be experimentally verified. Full article
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
Open AccessFeature PaperArticle Fourier’s Law in a Generalized Piston Model
Entropy 2017, 19(7), 350; doi:10.3390/e19070350
Received: 5 June 2017 / Revised: 3 July 2017 / Accepted: 6 July 2017 / Published: 11 July 2017
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Abstract
A simplified, but non trivial, mechanical model—gas of N particles of mass m in a box partitioned by n mobile adiabatic walls of mass M—interacting with two thermal baths at different temperatures, is discussed in the framework of kinetic theory. Following an
[...] Read more.
A simplified, but non trivial, mechanical model—gas of N particles of mass m in a box partitioned by n mobile adiabatic walls of mass M—interacting with two thermal baths at different temperatures, is discussed in the framework of kinetic theory. Following an approach due to Smoluchowski, from an analysis of the collisions particles/walls, we derive the values of the main thermodynamic quantities for the stationary non-equilibrium states. The results are compared with extensive numerical simulations; in the limit of large n, m N / M 1 and m / M 1 , we find a good approximation of Fourier’s law. Full article
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
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Open AccessArticle Information-Theoretic Bound on the Entropy Production to Maintain a Classical Nonequilibrium Distribution Using Ancillary Control
Entropy 2017, 19(7), 333; doi:10.3390/e19070333
Received: 23 March 2017 / Revised: 22 May 2017 / Accepted: 1 July 2017 / Published: 4 July 2017
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Abstract
There are many functional contexts where it is desirable to maintain a mesoscopic system in a nonequilibrium state. However, such control requires an inherent energy dissipation. In this article, we unify and extend a number of works on the minimum energetic cost to
[...] Read more.
There are many functional contexts where it is desirable to maintain a mesoscopic system in a nonequilibrium state. However, such control requires an inherent energy dissipation. In this article, we unify and extend a number of works on the minimum energetic cost to maintain a mesoscopic system in a prescribed nonequilibrium distribution using ancillary control. For a variety of control mechanisms, we find that the minimum amount of energy dissipation necessary can be cast as an information-theoretic measure of distinguishability between the target nonequilibrium state and the underlying equilibrium distribution. This work offers quantitative insight into the intuitive idea that more energy is needed to maintain a system farther from equilibrium. Full article
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
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Open AccessArticle Lyapunov Spectra of Coulombic and Gravitational Periodic Systems
Entropy 2017, 19(5), 238; doi:10.3390/e19050238
Received: 2 April 2017 / Revised: 15 May 2017 / Accepted: 15 May 2017 / Published: 20 May 2017
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Abstract
An open question in nonlinear dynamics is the relation between the Kolmogorov entropy and the largest Lyapunov exponent of a given orbit. Both have been shown to have diagnostic capability for phase transitions in thermodynamic systems. For systems with long-range interactions, the choice
[...] Read more.
An open question in nonlinear dynamics is the relation between the Kolmogorov entropy and the largest Lyapunov exponent of a given orbit. Both have been shown to have diagnostic capability for phase transitions in thermodynamic systems. For systems with long-range interactions, the choice of boundary plays a critical role and appropriate boundary conditions must be invoked. In this work, we compute Lyapunov spectra for Coulombic and gravitational versions of the one-dimensional systems of parallel sheets with periodic boundary conditions. Exact expressions for time evolution of the tangent-space vectors are derived and are utilized toward computing Lypaunov characteristic exponents using an event-driven algorithm. The results indicate that the energy dependence of the largest Lyapunov exponent emulates that of Kolmogorov entropy for each system for a given system size. Our approach forms an effective and approximation-free instrument for studying the dynamical properties exhibited by the Coulombic and gravitational systems and finds applications in investigating indications of thermodynamic transitions in small as well as large versions of the spatially periodic systems. When a phase transition exists, we find that the largest Lyapunov exponent serves as a precursor of the transition that becomes more pronounced as the system size increases. Full article
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
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Open AccessArticle Stochastic Stirling Engine Operating in Contact with Active Baths
Entropy 2017, 19(5), 193; doi:10.3390/e19050193
Received: 17 March 2017 / Revised: 10 April 2017 / Accepted: 21 April 2017 / Published: 27 April 2017
Cited by 3 | PDF Full-text (301 KB) | HTML Full-text | XML Full-text
Abstract
A Stirling engine made of a colloidal particle in contact with a nonequilibrium bath is considered and analyzed with the tools of stochastic energetics. We model the bath by non Gaussian persistent noise acting on the colloidal particle. Depending on the chosen definition
[...] Read more.
A Stirling engine made of a colloidal particle in contact with a nonequilibrium bath is considered and analyzed with the tools of stochastic energetics. We model the bath by non Gaussian persistent noise acting on the colloidal particle. Depending on the chosen definition of an isothermal transformation in this nonequilibrium setting, we find that either the energetics of the engine parallels that of its equilibrium counterpart or, in the simplest case, that it ends up being less efficient. Persistence, more than non-Gaussian effects, are responsible for this result. Full article
(This article belongs to the Special Issue Thermodynamics and Statistical Mechanics of Small Systems)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Memory effects in dissipative systems with conserved momentum
Author: Carlos A. Plata and Antonio Prados
Abstract: We consider a class of lattice models in which momentum is conserved in collisions whereas energy is not. These models can be considered as a simple picture for the shear component of the velocity of a granular fluid. Therein, we analyse the emergence of memory effects, like the so-called Kovacs effect, under different drivings. The dependence of these memory effects on both the driving mechanism and the system size is investigated in detail. The latter is specially relevant in the realm of granular systems, whose number of particles is not very large and fluctuation effects are expected to be important.

Title: Information-theoretic bound on the entropy production to maintain a classical nonequilibrium distribution
Author: Jordan Horowitz
Abstract: There are many functional contexts where it is desirable to maintain a mesoscopic system in a nonequilibrium state. However, such control requires an inherent energy dissipation. In this article, we unify and extend a number of works on the minimum energetic cost to maintain a mesoscopic system in a prescribed nonequilibrium distribution. For various control mechanisms, we find that the minimum amount of energy dissipation necessary can be cast as an information-theoretic measure of distinguishability between the target nonequilibrium state and the underlying equilibrium distribution. This work offers quantitative insight into the intuitive idea that more energy to maintain a system farther from equilibrium.

Author: Shamik Gupta and Stefano Ruffo
Title: Equilibration in the Nosé-Hoover isokinetic ensemble: Effect of inter-particle interactions
Abstract: We investigate the stationary and dynamic properties of the celebrated Nosé-Hoover dynamics of many-body interacting Hamiltonian systems, with an emphasis on the effect of inter-particle interactions. To this end, we consider a model system with both short- and long-range interactions. The Nosé-Hoover dynamics aims to generate the canonical equilibrium distribution of a system at a desired temperature by employing a set of time-reversible, deterministic equations of motion. A signature of canonical equilibrium is a single-particle momentum distribution that is Gaussian. We find that the equilibrium properties of the system within the Nosé-Hoover dynamics coincides with that within the canonical ensemble. Moreover, starting from out-of-equilibrium initial conditions, the average kinetic energy of the system relaxes to its target value over a size-independent timescale. However, quite surprisingly, our results indicate that under the same conditions and with only long-range interactions present in the system, the momentum distribution relaxes to its Gaussian form in equilibrium over a scale that diverges with the system size. On adding short-range interactions, the relaxation is found to occur over a timescale that has a much weaker dependence on system size. This system-size dependence of the timescale vanishes when only short-range interactions are present in the system. An implication of such an ultra-slow relaxation when only long-range interactions are present in the system is that macroscopic observables other than the average kinetic energy when estimated in the Nosé-Hoover dynamics may take an unusually long time to relax to its canonical equilibrium value. Our work underlines the crucial role that interactions play in deciding the equivalence between Nosé-Hoover and canonical equilibrium.

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