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Maxwell's Demon, 'a being whose faculties are so sharpened that he can follow every molecule in its course', has been the centre of much debate about its abilities to violate the second law of thermodynamics. Landauer's hypothesis, that the Demon must erase its memory and incur a thermodynamic cost, has become the standard response to Maxwell's dilemma, and its implications for the thermodynamics of computation reach into many areas of quantum and classical computing. It remains, however, still a hypothesis. Debate has often centred around simple toy models of a single particle in a box. Despite their simplicity, the ability of these systems to accurately represent thermodynamics (specifically to satisfy the second law) and whether or not they display Landauer Erasure, has been a matter of ongoing argument. The recent Norton-Ladyman controversy is one such example. In this paper we introduce a programming language to describe these simple thermodynamic processes, and give a formal operational semantics and program logic as a basis for formal reasoning about thermodynamic systems. We formalise the basic single-particle operations as statements in the language, and then show that the second law must be satisfied by any composition of these basic operations. This is done by finding a computational invariant of the system. We show, furthermore, that this invariant requires an erasure cost to exist within the system, equal to kTln2 for a bit of information: Landauer Erasure becomes a theorem of the formal system. The Norton-Ladyman controversy can therefore be resolved in a rigorous fashion, and moreover the formalism we introduce gives a set of reasoning tools for further analysis of Landauer erasure, which are provably consistent with the second law of thermodynamics.

Maxwell's Demon, 'a being whose faculties are so sharpened that he can follow every molecule in its course', has been the centre of much debate about its abilities to violate the second law of thermodynamics. Landauer's hypothesis, that the Demon must erase its memory and incur a thermodynamic cost, has become the standard response to Maxwell's dilemma, and its implications for the thermodynamics of computation reach into many areas of quantum and classical computing. It remains, however, still a hypothesis. Debate has often centred around simple toy models of a single particle in a box. Despite their simplicity, the ability of these systems to accurately represent thermodynamics (specifically to satisfy the second law) and whether or not they display Landauer Erasure, has been a matter of ongoing argument. The recent Norton-Ladyman controversy is one such example. In this paper we introduce a programming language to describe these simple thermodynamic processes, and give a formal operational semantics and program logic as a basis for formal reasoning about thermodynamic systems. We formalise the basic single-particle operations as statements in the language, and then show that the second law must be satisfied by any composition of these basic operations. This is done by finding a computational invariant of the system. We show, furthermore, that this invariant requires an erasure cost to exist within the system, equal to kTln2 for a bit of information: Landauer Erasure becomes a theorem of the formal system. The Norton-Ladyman controversy can therefore be resolved in a rigorous fashion, and moreover the formalism we introduce gives a set of reasoning tools for further analysis of Landauer erasure, which are provably consistent with the second law of thermodynamics.

Thermodynamics-dependent microstructure, phase, and physical model predictions of material characteristics are demonstrated for aluminum alloys 7020 (Al-4.5Zn-1.2Mg), 7039 (Al-4.0Zn-2.8Mg), and 7075 (Al-5.6Zn-2.5Mg-1.6Cu) by direct application of Sente Software Ltd. s Java Materials Program (JMatPro) mesoscale computation materials engineering software. JMatPro reveals phase constitutions as a function of input composition, temperature, and time; with the use of material property databases and physical models, it calculates temperature-dependent physical and mechanical properties. The JMatPro material property software provides better and more rapid understanding of materials during research, processing, product manufacture, and service. In this report, JMatPro reveals how structural and protection materials may meet design requirements for low cost, fabricability, and durability. With secondary application, the elastic bulk moduli for intermetallic phase inclusions derived from Gibbs energy by JMatPro are used to predict the maximum levels of microscale shear stresses under hydrostatic pressure. With comparison to conditions known to cause incipient spall in 7020 alloy, the levels of microscale shear stress around intermetallic inclusions are shown to equal or exceed the level of Von Mises calculated shear yield strength of 7020 alloy, revealing that deformation may occur during high load spall events, even at the initial stages of compression.

Living cells use readout molecules to record the state of receptor proteins, similar to measurements or copies in typical computational devices. But is this analogy rigorous? Can cells be optimally efficient, and if not, why? We show that, as in computation, a canonical biochemical readout network generates correlations; extracting no work from these correlations sets a lower bound on dissipation. For general input, the biochemical network cannot reach this bound, even with arbitrarily slow reactions or weak thermodynamic driving. It faces an accuracy-dissipation trade-off that is qualitatively distinct from and worse than implied by the bound, and more complex steady-state copy processes cannot perform better. Nonetheless, the cost remains close to the thermodynamic bound unless accuracy is extremely high. Additionally, we show that biomolecular reactions could be used in thermodynamically optimal devices under exogenous manipulation of chemical fuels, suggesting an experimental system for testing computational thermodynamics.

We have developed a methodology to study the thermodynamics of order-disorder transformations in n-component substitutional alloys that combines nonequilibrium methods, which can efficiently compute free energies, with Monte Carlo simulations, in which configurational and vibrational degrees of freedom are simultaneously considered on an equal footing basis. Furthermore, by appropriately constraining the system, we were able to compute the contributions to the vibrational entropy due to bond proportion, atomic size mismatch, and bulk volume effects. We have applied this methodology to calculate configurational and vibrational contributions to the entropy of the Ni3Al alloy as functions of temperature. We found that the bond proportion effect reduces the vibrational entropy at the order-disorder transition, while the size mismatch and the bond proportion effects combined do not change the vibrational entropy at the transition. We also found that the volume increase at the order-disorder transition causes a vibrational entropy increase of 0.08 kB/atom, which is significant when compared to the configurational entropy increase of 0.27 kB/atom. Our calculations indicate that the inclusion of vibrations reduces in about 30 percent the order-disorder transition temperature determined solely considering the configurational degrees of freedom.

We have developed a methodology to study the thermodynamics of order-disorder transformations in n-component substitutional alloys that combines nonequilibrium methods, which can efficiently compute free energies, with Monte Carlo simulations, in which configurational and vibrational degrees of freedom are simultaneously considered on an equal footing basis. Furthermore, by appropriately constraining the system, we were able to compute the contributions to the vibrational entropy due to bond proportion, atomic size mismatch, and bulk volume effects. We have applied this methodology to calculate configurational and vibrational contributions to the entropy of the Ni3Al alloy as functions of temperature. We found that the bond proportion effect reduces the vibrational entropy at the order-disorder transition, while the size mismatch and the bond proportion effects combined do not change the vibrational entropy at the transition. We also found that the volume increase at the order-disorder transition causes a vibrational entropy increase of 0.08 kB/atom, which is significant when compared to the configurational entropy increase of 0.27 kB/atom. Our calculations indicate that the inclusion of vibrations reduces in about 30 percent the order-disorder transition temperature determined solely considering the configurational degrees of freedom.

The Law of Optimized Complexity: A Computational Twin to the Second Law of Thermodynamics for Sustainable Intelligence Design Berend Watchus first published as preprint on Zenodo.org on July 17, 2025 DOI : 10.5281/zenodo.16029079