Hidden Dissipation and Irreversibility in Maxwell’s Demon

Maxwell’s demon is an entity in a 150-year-old thought experiment that paradoxically appears to violate the second law of thermodynamics by reducing entropy without doing work. It has increasingly practical implications as advances in nanomachinery produce devices that push the thermodynamic limits imposed by the second law. A well-known explanation claiming that information erasure restores second law compliance fails to resolve the paradox because it assumes the second law a priori, and does not predict irreversibility. Instead, a purely mechanical resolution that does not require information theory is presented. The transport fluxes of mass, momentum, and energy involved in the demon’s operation are analyzed and show that they imply “hidden” external work and dissipation. Computing the dissipation leads to a new lower bound on entropy production by the demon. It is strictly positive in all nontrivial cases, providing a more stringent limit than the second law and implying intrinsic thermodynamic irreversibility. The thermodynamic irreversibility is linked with mechanical irreversibility resulting from the spatial asymmetry of the demon’s speed selection criteria, indicating one mechanism by which macroscopic irreversibility may emerge from microscopic dynamics.

Modelling the Demand and Access of Mineral Resources in a Changing World

Humanity is using mineral resources at an unprecedented level and demand will continue to grow over the next few decades before stabilizing by the end of the century, due to the economic development of populated countries and the energy and digital transitions. The demand for raw materials must be estimated with a bottom-up and regionalised approach and the supply capacity with approaches coupling long-term prices with energy and production costs controlled by the quality of the resource and the rate of technological improvement that depends on thermodynamic limits. Such modelling provides arguments in favour of two classically opposed visions of the future of mineral resources: an unaffordable increase in costs and prices following the depletion of high quality deposits or, on the contrary, a favourable compensation by technological improvements. Both views are true, but not at the same time. After a period of energy and production cost gains, we now appear to be entering a pivotal period of long-term production cost increases as we approach the minimum practical energy and thermodynamic limits for many metals.

Thermodynamic limits for assimilation of silicate crust in primitive magmas

Some geochemical models for basaltic and more primitive rocks suggest that their parental magmas have assimilated tens of weight percent of crustal silicate wall rock. But what are the thermodynamic limits for assimilation in primitive magmas? We pursue this question quantitatively using a freely available thermodynamic tool for phase equilibria modeling of open magmatic systems—the Magma Chamber Simulator (https://mcs.geol.ucsb.edu)—and focus on modeling assimilation of wall-rock partial melts, which is thermodynamically more efficient compared to bulk assimilation of stoped wall-rock blocks in primitive igneous systems. In the simulations, diverse komatiitic, picritic, and basaltic parental magmas assimilate progressive partial melts of preheated average lower, middle, and upper crust in amounts allowed by thermodynamics. Our results indicate that it is difficult for any subalkaline primitive magma to assimilate more than 20–30 wt% of upper or middle crust before evolving to compositions with higher SiO2 than a basaltic magma (52 wt%). On the other hand, typical komatiitic magmas have thermodynamic potential to assimilate as much as their own mass (59–102 wt%) of lower crust and retain a basaltic composition. The compositions of the parental melt and the assimilant heavily influence both how much assimilation is energetically possible in primitive magmas and the final magma composition given typical temperatures. These findings have important implications for the role of assimilation in the generation and evolution of, e.g., ultramafic to mafic trans-Moho magmatic systems, siliceous high-Mg basalts, and massif-type anorthosites.

Exploring the Thermodynamic Limits of Enhanced H2 Recovery With Inherent Carbon Removal From Low Value Aqueous Biomass Oxygenate Precursors

Rational integration of chemical pathways at the molecular scale to direct thermodynamically favorable enhanced H2 production with inherent carbon removal from low-value substrates can be guided by exploring the thermodynamic limits of feasibility. The substrates of interest are biomass oxygenates that are water-soluble and uneconomical for separation from water. In this study, we investigate the thermodynamic feasibility of recovering H2 with inherent carbon removal from biomass oxygenates such as ethanol, methanol, glycerol, ethylene glycol, acetone, and acetic acid. The influence of biomass oxygenate-to-water ratios, reaction temperature of 150°C–325°C, and CaO or Ca(OH)2 as the alkalinity source on the yields of H2, CH4, CO2, and Ca-carbonate are investigated. By maintaining the fluids in the aqueous phase under pressure, energy needs associated with vaporization are circumvented. The hypothesis that enhanced alkalinity favors the preferential formation of CO (precursor for CO2 formation) over CH4 and aids the formation of calcium carbonate is investigated. The findings from these studies inform the feasibility, design of experiments, and the tuning of reaction conditions for enhanced H2 recovery with inherent carbon removal from biomass oxygenate sources.

Supplemental Material: Thermodynamic limits for assimilation of silicate crust in primitive magmas

Supplemental discussion on the MCS model parameters, and all model input and output.<br>

Supplemental Material: Thermodynamic limits for assimilation of silicate crust in primitive magmas

Supplemental discussion on the MCS model parameters, and all model input and output.<br>

Fishnet four-point integrals: integrable representations and thermodynamic limits

We consider four-point integrals arising in the planar limit of the conformal “fishnet” theory in four dimensions. They define a two-parameter family of higher-loop Feynman integrals, which extend the series of ladder integrals and were argued, based on integrability and analyticity, to admit matrix-model-like integral and determinantal representations. In this paper, we prove the equivalence of all these representations using exact summation and integration techniques. We then analyze the large-order behaviour, corresponding to the thermodynamic limit of a large fishnet graph. The saddle-point equations are found to match known two-cut singular equations arising in matrix models, enabling us to obtain a concise parametric expression for the free-energy density in terms of complete elliptic integrals. Interestingly, the latter depends non-trivially on the fishnet aspect ratio and differs from a scaling formula due to Zamolodchikov for large periodic fishnets, suggesting a strong sensitivity to the boundary conditions. We also find an intriguing connection between the saddle-point equation and the equation describing the Frolov-Tseytlin spinning string in AdS3 × S1, in a generalized scaling combining the thermodynamic and short-distance limits.