Linear response in large deviations theory: A method to compute non-equilibrium distributions

AbstractThe effect of the temperature gradient on the Soret coefficient in n-pentane/n-decane (n-C5/n-C10) mixtures was investigated using non-equilibrium molecular dynamics (NEMD) with the heat exchange (eHEX) algorithm. n-Pentane/n-decane mixtures with three different compositions (0.25, 0.5, and 0.75 mole fractions, respectively) and the TraPPE-UA force field were used in computing the Soret coefficient ({S_{T}}) at 300 K and 1 atm. Added/removed heat quantities (ΔQ) of 0.002, 0.004, 0.006, 0.008, and 0.01 kcal/mol were employed in eHEX processes in order to study the effect of different thermal gradients on the Soret coefficient. Moreover, a phenomenological description was applied to discuss the mechanism of this effect. Present results show that the Soret coefficient values firstly fluctuate violently and then become increasingly stable with increasing ΔQ (especially in the mixture with a mole fraction of 0.75), which means that ΔQ has a smaller effect on the Soret coefficient when the temperature gradient is higher than a certain thermal gradient. Thus, a high temperature gradient is recommended for calculating the Soret coefficient under the conditions that a linear response and constant phase are ensured in the system. In addition, the simulated Soret coefficient obtained at the highest ΔQ within three different compositions is in great agreement with experimental data.

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Response theory and phase transitions for the thermodynamic limit of interacting identical systems

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2020.0688 ◽

2020 ◽

Vol 476 (2244) ◽

pp. 20200688

Author(s):

Valerio Lucarini ◽

Grigorios A. Pavliotis ◽

Niccolò Zagli

Keyword(s):

Phase Transitions ◽

Thermodynamic Limit ◽

Linear Response ◽

Equilibrium Phase ◽

Mean Field ◽

Critical Transitions ◽

Autocorrelation Time ◽

The Common ◽

Fokker Planck Equations ◽

Non Equilibrium

We study the response to perturbations in the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non-equilibrium conditions. All systems are nudged towards the common centre of mass. We derive Kramers–Kronig relations and sum rules for the linear susceptibilities obtained through mean field Fokker–Planck equations and then propose corrections relevant for the macroscopic case, which incorporates in a self-consistent way the effect of the mutual interaction between the systems. Such an interaction creates a memory effect. We are able to derive conditions determining the occurrence of phase transitions specifically due to system-to-system interactions. Such phase transitions exist in the thermodynamic limit and are associated with the divergence of the linear response but are not accompanied by the divergence in the integrated autocorrelation time for a suitably defined observable. We clarify that such endogenous phase transitions are fundamentally different from other pathologies in the linear response that can be framed in the context of critical transitions. Finally, we show how our results can elucidate the properties of the Desai–Zwanzig model and of the Bonilla–Casado–Morillo model, which feature paradigmatic equilibrium and non-equilibrium phase transitions, respectively.

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