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Open research questions in Advanced Thermodynamics and Statistical Mechanics

74 unresolved questions extracted from the limitations and future-work sections of 287 Advanced Thermodynamics and Statistical Mechanics papers in our library. Each links back to the study that raised it.

What the literature leaves open

  • The problem of studying the evolution of the energy at time N 2 t in the limit N → ∞ for ε small, but fixed, needs to be addressed. The result of this paper can be used as a starting point for further research on the behavior of deterministic systems.

    Heat equation from a deterministic dynamics · 2026 · DOI

  • The problem of studying the evolution of the energy at time N 2 t in the limit N → ∞ for ε small, but fixed, is extremely hard and not tackled in this paper. The derivation of macroscopic PDE evolution laws from microscopic ones is a well-posed problem that needs to be addressed.

    Heat equation from a deterministic dynamics · 2026 · DOI

  • The need to generate ultralong, densely entangled chains. The need to create a material that is fully deconstructable and reprocessable. The need to preserve the topological class of the network during regeneration.

    Chain entanglements enable regeneration of high-performance thermosets · 2026 · DOI

  • The non-Markovian dynamics of the system. The need for a theoretical framework to study the fluctuations of entropy production. The complexity of the generalized Langevin equation.

    Entropy-production fluctuation theorem for a generalized Langevin particle in crossed electric and magnetic fields · 2026 · DOI

  • The paper suggests that future research should focus on deploying the OECQ-V2 algorithm on an industrial site. The paper suggests that future research should investigate the application of the framework to other problems.

    Réalisation physique finie des circuits quantiques Version 2 — Cadre thermodynamique informationnel et partitionnement modulaire à l'échelle de 100 qubits PROJET OECQ — Optimisation Énergétique des Circuits Quantiques · 2026 · DOI

  • The paper identifies a gap in the development of quantum circuits, specifically the need for a framework that can manage quantum sobriety. The paper identifies a gap in the scaling up of quantum circuits to 100 qubits and photonics modes.

    Réalisation physique finie des circuits quantiques Version 2 — Cadre thermodynamique informationnel et partitionnement modulaire à l'échelle de 100 qubits PROJET OECQ — Optimisation Énergétique des Circuits Quantiques · 2026 · DOI

  • Further development of the method to apply to more complex systems. Experimental verification of the method. Application of the method to a variety of fields.

    A method for calculating entropy production without knowing transition rates or dwell times · 2026 · DOI

  • Prior work has focused on calculating entropy production rate from knowledge of underlying dynamics. There is a need for a method that can infer entropy production rate without knowledge of transition rates or dwell times.

    A method for calculating entropy production without knowing transition rates or dwell times · 2026 · DOI

  • Although numerically exact methods can simulate this non-monotonic behavior, they offer limited information on the thermal state of the heat baths.

    Probing Non-equilibrium baths: Frequency-Resolved Thermometry and Quantum Heat Current Turnover · 2026

  • We show that the electronic response of a tungsten cascade is sparse, structured, and regime dependent, rather than representable by a single scalar damping coefficient, and that whereas the equilibrium phonon linewidth reduction supports an equilibrium Langevin closure for thermal lattice motion, the driven stopping reduction provides a deterministic loss law for ballistic recoils.

    Electronic energy loss in tungsten collision cascades: A quantum statistical study of force scales, friction, and stopping · 2026 · DOI

  • The study focuses on theoretical analysis of quantum heat engines with Unruh-DeWitt detectors; experimental validation of the predicted thermodynamic and quantum correlation behaviors in realistic systems remains an open challenge.

    Quantum thermodynamics, quantum correlations and quantum coherence in accelerating Unruh–DeWitt detectors in both steady and dynamical state · 2026 · DOI

  • Instead of attempting to measure the Unruh temperature directly, future work should look for indirect signatures in quantum resources such as entanglement or coherence generated through field-mediated correlations between detectors, as such resource-based signatures may provide more experimentally accessible indicators.

    Quantum thermodynamics, quantum correlations and quantum coherence in accelerating Unruh–DeWitt detectors in both steady and dynamical state · 2026 · DOI

  • Traditional teaching methods focus heavily on derivation work and regular exercises, which restricts students' conceptual comprehension and reduces the link between theoretical knowledge and real physical situations.

    From Equations to Real Problems: A Problem-Based Reform of Thermodynamics and Statistical Physics Teaching in Higher Education · 2026 · DOI

  • The paper notes that some students accustomed to lecture-centered teaching may need time to adjust to problem-based learning, but provides no longitudinal data on the duration of this transition period, the specific demographic characteristics of students who struggle with the adjustment, or what pedagogical scaffolding mechanisms should be implemented to support this transition in thermodynamics courses.

    From Equations to Real Problems: A Problem-Based Reform of Thermodynamics and Statistical Physics Teaching in Higher Education · 2026 · DOI

  • Equilibrium physics (EQP) has long stood as principled, powerful and versatile. And although EQP is limited by nearness to equilibria, it’s two-laws structure has long been seen as the key to an ultimately more general framework for arbitrary non-equilibria. Here, we achieve this in CFT for network flows by switching the conceptual framework: (i) from state entropies to path entropies, and (ii) from complete observable sets such as (U, V, N) to complete observable sets of distributions and fluxes (π, τ, J). This now unlocks the same mathematical power as EQP has—i.e., of Legendre transforms and Maxwell-like relations and fluctuation-response relations for general conjugate variable pairs, now for forces and flows. A virtue of CFT—stemming from its foundation in entropy as envisioned by pioneers, like Szilárd and Jaynes and others43–46—is its ability to go beyond thermal processes, like heat and work and particle flows, to also model the transport of any mobile agent. ACKNOWLEDGMENTS We thank Charles Kocher, Olga Movilla Miangolarra, Jonathan Pachter, Rostam Razban, Yuhai Tu, Lakshmanji Verma, and Jin Wang for insightful feedback. Y.-J. expresses his deepest gratitude to Hong Qian for guiding him in learning the essential theoretical pieces used in this work. We are grateful for the financial support from the Laufer Center for Physical and Quantitative Biology at Stony Brook, the John Templeton Foundation (Grant ID 62564), and NIH (Grant RM1- GM135136). REFERENCE 1H. Touchette, “The large deviation approach to statistical mechanics,” Physics Reports 478, 1–69 (2009). 2K. Huang, Statistical Mechanics, 2nd Edition, 2nd ed. (Wiley, New York, 1987). 3L. D. Landau and E. M. Lifshitz, Statistical Physics, Third Edition, Part 1: Volume 5, 3rd ed. (Butterworth-Heinemann, Amsterdam u.a, 1980). 4J. A. Pachter and K. A. Dill, “Nonequilibrium statistical physics beyond the ideal heat bath approximation,” Phys. Rev. E 107, 014131 (2023). 5J. A. Pachter, Y.-J. Yang, and K. A. Dill, “Entropy, irreversibility and inference at the foundations of statistical physics,” Nat Rev Phys, 1–12 (2024). 6E. T. Jaynes, “The Minimum Entropy Production Principle,” Annual Review of Physical Chemistry 31, 579–601 (1980). 7R. M. L. Evans, “Rules for Transition Rates in Nonequilibrium Steady States,” Phys. Rev. Lett. 92, 150601 (2004). 8S. Pressé, K. Ghosh, J. Lee, and K. A. Dill, “Principles of maximum entropy and maximum caliber in statistical physics,” Rev. Mod. Phys. 85, 1115–1141 (2013). 5 9S. Davis, D. González, and G. Gutiérrez, “Probabilistic Inference for Dynamical Systems,” Entropy 20, 696 (2018). 10C. Maes and K. Netoˇcný, “Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states,” EPL 82, 30003 (2008). 11C. Maes, “Frenesy: Time-symmetric dynamical activity in nonequilibria,” Physics Reports 850, 1–33 (2020). 12J.

    A principled basis for nonequilibrium network flows · 2026 · DOI

  • This asymmetry between Carnot engines and Carnot refrigerators, though established in formal thermodynamics, is frequently overlooked or misunderstood by students, indicating a lack of accessible physical (non-entropy-based) explanations.

    From optimal engines to minimal refrigerators: the Carnot case · 2026 · DOI

  • Further studies can explore the application of the proposed optimal control strategies to other systems. The development of new experimental techniques to verify the theoretical predictions.

    Optimal Protocols for Minimizing Entropy Production in Finite-Time Stochastic Thermodynamics · 2026 · DOI

  • The gap between transient evolution and steady-state transport remains unaddressed. The lack of a comprehensive theoretical framework for dissipation optimization in finite-time operations and non-equilibrium steady states.

    Optimal Protocols for Minimizing Entropy Production in Finite-Time Stochastic Thermodynamics · 2026 · DOI

  • The extension of the theory to include generic POVMs. The experimental realization of the measurement process and the study of its thermodynamic cost. The optimization of measurement projectors and feedback unitaries for maximum Landauer efficiency.

    Impact of information on quantum heat engines · 2026 · DOI

  • The lack of a general framework for feedback-controlled thermal machines. The need to take into account the thermodynamic cost of information gathering in quantum thermal engines.

    Impact of information on quantum heat engines · 2026 · DOI

  • The quasi-static assumption: the derivation of Ṡgas = (dE + P dV)/T assumes the gas remains near local thermodynamic equilibrium. Opacity and photon trapping: if the system is optically thick, photons are temporarily trapped and the effective T rad at the photosphere can be much lower than the interior temperature.

    Entropy, gravity, and an apparent violation of the second law · 2026 · DOI

  • Studying other physical properties of learning processes beyond energy cost. Exploring the implications of the results for energy storage, manipulation, and transfer. Investigating the potential applications of the results to black holes.

    Learning to erase quantum states: thermodynamic implications of quantum learning theory · 2026 · DOI

  • The lack of understanding of the physical consequences of abstract learning processes. The lack of efficient thermodynamic protocols based on learning. The lack of a concrete connection between quantum learning theory and thermodynamics.

    Learning to erase quantum states: thermodynamic implications of quantum learning theory · 2026 · DOI

  • The lack of a consistent quantum theory of heat flow. The insufficient textbook expression for heat flow. The need for a resolution of the paradoxical behavior in the textbook formula.

    Entropy Flow at the Quantum Limit · 2026 · DOI

  • To study the effects of qubit interactions and asymmetric couplings to the baths on the geometric heat pumping. To apply the approach to more complex systems and to study the scalability of the results. To explore the potential applications of the findings in quantum thermal machines.

    Lindbladian approach for many-qubit thermal machines: Enhancing the performance with geometric heat pumping by interaction · 2026 · DOI

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74 open questions have been extracted from the limitations and future-work passages of 287 Advanced Thermodynamics and Statistical Mechanics papers in our library. Each one below links back to the study that raised it, so you can read the original claim in context.

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