American Scientist

To the Editors:

Daniel P. Sheehan’s article “Maxwell Zombies: Conjuring the Thermodynamic Undead” (July–August) does not address several questions that are crucial to his thesis that the second law of thermodynamics is not absolute.

First, in the two-thermocouple test of Duncan’s paradox, the inability of gas-phase reactions to establish normal gas-phase equilibrium was discussed. However, nothing was mentioned about the effects of hydrogen monomer dissolution in tungsten and in rhenium; the equilibrium, or lack thereof, of the monomers in the solid solution; or the migration of the monomers away from the catalytic surface, possibly into the thermocouples (the thermoelectric properties of which might change) or out of the core.

Second, in the discussion of the temperature zombie, it is postulated that one surface preferentially splits molecules while another preferentially combines them under steady-state conditions, but no account is taken of the fact that these reactions are reversible. Once the concentrations of dissolved molecules and dissociated parts of molecules in the gas have reached a steady state, an equilibrium should be reached in which the catalyst dissociates and recombines molecules at the same rate, and the relative concentrations of dissociated species and combined molecules in the gas are equal to those that exist in equilibrium without a catalyst. This ratio depends on the temperature and pressure of the gas rather than on the properties of the catalyst. Therefore, surfaces S1 and S2 should both be in equilibrium with the gas, and each should be splitting molecules at the same rate as it is combining molecules. Neither surface should be cooling by dissociating molecules at a rate faster than the rate at which it is combining molecules, and neither surface should be warming by recombining molecules faster than the rate at which it is dissociating them.

Have these phenomena of gas dissolution in the catalyst and the reversibility of the catalytic reactions been thoroughly accounted for?

Edward B. Stoneham
Los Altos, CA

Dr. Sheehan responds:

Dr. Stoneham raises two pertinent issues. To the first, rhenium and tungsten metals dissolve and diffuse hydrogen molecules and atoms to negligible extents, and Type C (tungsten-rhenium) thermocouples are not known to absorb or dissolve hydrogen, nor are their Seebeck coefficients known to be affected by hydrogen at these temperatures or pressures; quite to the contrary, these thermocouples are specifically called for in cases of reducing atmospheres like this. Moreover, the thermocouples measurements were corroborated by optical pyrometer measurements in a series of complementary hydrogen-metal experiments. (See Foundations of Physics 44:235 for details.) Second, it is asserted that the epicatalysts should behave like catalysts and thereby promote an equilibrium that depends only on gas pressure and temperature, not on surface type. Actually, it is precisely this tenet—that catalysts cannot shift the gas phase equilibrium of a reaction—that epicatalysts specifically break, thereby allowing their anomalous thermodynamic behavior. Fuller theoretical explanations of epicatalysis are in Physical Review E 88:032125, Physical Review E 57:6660, Journal of Nonequilibrium Thermodynamics (2018; doi:10.1515/jnet-2017-0007); additional experimental support can be found in Reviews of Scientific Instrumentation 87:074101.

To the Editors:

In Daniel P. Sheehan’s article, he describes Maxwell zombies whose behaviors violate the second law of thermodynamics. I’d like to point out that Maxwell zombies are created via epicatalysis, a nonequilibrium phenomenon in which a catalyst changes the distribution of reactant states and product states via nonequilibrium noise. The second law of thermodynamics concerns equilibria; this law does not govern nonequilibrium behaviors. Therefore, Maxwell zombies do not violate the second law of thermodynamics.

On a side note, had epicatalysis been discovered in systems at equilibrium, Maxwell zombies would be equivalent to Maxwell demons as these zombies could also lower the entropy of an isolated system by altering the chemical equilibrium.

Yingbin Ge
Central Washington University
Ellensburg, WA

Dr. Sheehan responds:

Dr. Ge raises an issue at the heart of thermodynamics: What does the second law actually say?

In our monograph, Challenges to the Second Law of Thermodynamics: Theory and Experiment, (Springer, Fundamentals of Physics series, 2005) Vladislav Capek and I cite 21 different versions of it—without exhausting the well.

Some versions refer to equilibrium, whereas others do not. The oft-cited Planck formulation states: The entropy change of the universe for any natural (spontaneous) process is never negative. This applies to any macroscopic process or system, whether at equilibrium or nonequilibrium. Heat engines are examples of nonequilibrium systems that transform heat into work while generating entropy. Second law violators (zombies) are also nonequilibrium systems, transforming thermal energy into work, but with the net effect of reducing the net entropy of the universe, thus violating the Planck formulation (as well as others).