Fluctuations in partitioning systems with few degrees of freedom

Cerino, Luca; Gradenigo, Giacomo; Sarracino, Alessandro; Villamaina, Dario; Vulpiani, Angelo

doi:10.1103/physreve.89.042105

Cited by 9 publications

(18 citation statements)

References 28 publications

(36 reference statements)

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“…(1a) and the original eq. A1 in [10] don't have the same last term. Such discrepancy is due to a confirmed misprint [1] in [10].…”

Section: Introductionmentioning

confidence: 99%

Multiple scales approach to the gas-piston non-equilibrium themodynamics

Chiuchiù¹,

Gubbiotti²

2016

J. Stat. Mech.

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The non-equilibrium thermodynamics of a gas inside a piston is a conceptually simple problem where analytic results are rare. For example, it is hard to find in the literature analytic formulas that describe the heat exchanged with the reservoir when the system either relaxes to equilibrium or is compressed over a finite time. In this paper we derive such kind of analytic formulas. To achieve this result, we take the equations derived by Cerino et al. [Phys. Rev. E 91, 032128] describing the dynamic evolution of a gas-piston system, we cast them in a dimensionless form and we solve the dimensionless equations with the multiple scales expansion method. With the approximated solutions we obtained, we express in a closed form the heat exchanged by the gas-piston system with the reservoir for a large class of relevant non-equilibrium situations.

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“…(1a) and the original eq. A1 in [10] don't have the same last term. Such discrepancy is due to a confirmed misprint [1] in [10].…”

Section: Introductionmentioning

confidence: 99%

Multiple scales approach to the gas-piston non-equilibrium themodynamics

Chiuchiù¹,

Gubbiotti²

2016

J. Stat. Mech.

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“…The stochastic part is obtained by adding the Gaussian noise terms with amplitudes determined by imposing that the variances of the variables coincide with those computed within the canonical ensemble [17]. This yields …”

Section: ~ ~ M + X J Dv (M + ~ V)ft{mentioning

confidence: 99%

Kinetic model for the finite-time thermodynamics of small heat engines

2015

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We study a molecular engine constituted by a gas of N∼102 molecules enclosed between a massive piston and a thermostat. The force acting on the piston and the temperature of the thermostat are cyclically changed with a finite period τ. In the adiabatic limit τ→∞, even for finite size N, the average work and heat reproduce the thermodynamic values, recovering the Carnot result for the efficiency. The system exhibits a stall time τ* where the net work is zero: for τ<τ* it consumes work instead of producing it, acting as a refrigerator or as a heat sink. At τ>τ* the efficiency at maximum power is close to the Curzorn-Ahlborn limit. The fluctuations of work and heat display approximatively a Gaussian behavior. Based upon kinetic theory, we develop a three-variables Langevin model in which the piston's position and velocity are linearly coupled together with the internal energy of the gas. The model reproduces many of the system's features, such as the inversion of the work's sign, the efficiency at maximum power, and the approximate shape of the fluctuations. A further simplification in the model allows us to compute analytically the average work, explaining its nontrivial dependence on τ.

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“…The effective force acting on the piston due to the collisions with gas particles, appearing in Equation (20), is given by two contributions, F coll = F L coll + F R coll . By taking into account the elastic collisions rule, Equation (1), these terms can be computed as follows:…”

Section: Piston Positionmentioning

confidence: 99%

“…The system at its ends interacts with thermal baths at fixed temperatures. It is easy to realize the analogy between such a generalized piston model and the systems of masses and springs: the pistons and the gas compartments play the role of masses and springs, respectively.Our model is an example of partitioning system (as the adiabatic piston), where previous studies showed that the presence of mobile walls can induce interesting behaviours [12][13][14][15][16][17][18][19][20][21]. Basically, in the study of partitioning systems, one can adopt two approaches: in terms of a Boltzmann equation [14] or introducing effective equations (Langevin-like) for suitable observables derivedà la Smoluchowski, i.e., from an analysis of the collisions particles/walls.…”

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confidence: 99%

Fourier’s Law in a Generalized Piston Model

Caprini

Cerino

Sarracino

et al. 2017

Entropy

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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, mN/M 1 and m/M 1, we find a good approximation of Fourier's law.

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Fluctuations in partitioning systems with few degrees of freedom

Cited by 9 publications

References 28 publications

Multiple scales approach to the gas-piston non-equilibrium themodynamics

Multiple scales approach to the gas-piston non-equilibrium themodynamics

Kinetic model for the finite-time thermodynamics of small heat engines

Fourier’s Law in a Generalized Piston Model

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