Dr. Purushottam D. Gujrati

Physics, Polymer Science

Theoretical Physics, Nonequilibrium Statistical Thermodynamics, and Condensed Matter Physics

Contact

  • Email: pdg@uakron.edu
  • Phone: 330-972-7136
  • Location: Room 327, Polymer Engineering Academic Center, The University of Akron

Education

  • M.A., Physics – Columbia University, N.Y., N.Y. –1974
  • M.Phil., Physics – Columbia University, N.Y., N.Y. –1979
  • Ph.D., Physics – Columbia University, N.Y., N.Y. – 1979
  • Post-doc – Yeshiva University, N.Y., N.Y. –1978-1979
  • Post-doc – Carnegie-Mellon, Pittsburgh, PA – 1979-1981
  • Post-doc – University of Chicago, Chicago, ILL – 1981-1983
  • Faculty, University of Akron, Akron, OH – 1983-present

Research Interests

  • Phase transitions and critical phenomena
  • Polymer physics
  • Combinatorics and graph theory
  • Renormalization group and field theory
  • Rigorous statistical mechanics on recursive lattices
  • Nonuniformity and unique internal variables
  • Nonequilibrium Processes
  • Extended state space for irreversibility
  • Mechanical origin of the generalized second law

Selected Recent Publications and Significance

  • P.D. Gujrati, Operational Extension of the Carnot-Clausius Construct to Nonequilibrium Entropy and the Second Law for Positive and Negative Temperatures, Entropie thermodynamique – énergie – environnement – économie: n° Spécial LILA 3, 7(2):1-96 (2026), DOI:10.21494/ISTE.OP.2026.1433

    This publication is a review of a part of my journey including glasses in nonequilibrium statistical thermodynamics over the last fifteen years or so.

  • P.D. Gujrati, Carnot Theorem Revisited: A Critical Perspective, Entropy 27(4): 346 (2025), DOI: 10.3390/e27040346

    In this critical evaluation of the contribution by Carnot to thermodynamics, I have argued against the incorrect identification of caloric with entropy, which is still being propagated by various workers. Additionally, while everyone agrees about his important contribution to the modern understanding of irreversibility and the second law, I have also taken liberty with the prevalent understanding during his time and modern understanding of his contribution by various authors to suggest that he was also familiar with the first law for an isolated system. I also clarify other misunderstandings of his contribution.

  • P.D. Gujrati, Irreversibility, Dissipation, and Its Measure: A New Perspective, Symmetry 17(2): 232 (20125)  DOI:10.3390/sym17020232

    I identify dissipation D through fundamental thermodynamic constraint diW= diQ≥0 for all spontaneously irreversible processes and all temperatures T, positive and negative in an isolated system.  It follows from the generalized second law (GSL). As T plays an important role in the quantification, dissipation allows for ∆iS≥0 for T>0 and ∆iS<0 for T<0, a very surprising result. The Kullback–Leibler distance is shown to be non-thermodynamic, so it cannot be equated with D as is commonly done. The determination of D requires dipk. The Fokker-Planck and master equations are not general enough to determine it. We modify the Fokker-Planck equation to fix the issue.

  • P.D. Gujrati, Mechanical Foundations of the Generalized Second Law and the Irreversibility Principle, Foundations 4(4):560-592 (2024), DOI:10.3390/foundations4040037

    The Boltzmann-Carnot-Clausius-Gibbs-Maxwell (BCGM) proposal treats a thermodynamic system as a collection of microstates of a mechanical system appended by microstate probabilities. It is used to establish the generalized second law (GSL) that is applicable to a system of any size, including a single particle system as our example establishes, and that supersedes the celebrated second law of increase of entropy of an isolated system. GSL is merely a consequence of the mechanical equilibrium (stable or unstable) principle of analytical mechanics and the first law. An irreversibility principle that covers all processes, spontaneous or not, and that have both positive and negative nonequilibrium temperatures T is also justified.

  • P.D. Gujrati, Non-Equilibrium Entropy in an Extended State Space, in Frontier in Entropy Across the Disciplines: Panorama of Entropy: Theory, Computation, and Applications (2022), pp. 627-669, ed. W. Freeden and M Zuhair Nashed, DOI:10.1142/9789811259401_0018

    Non-Equilibrium Entropy in an Extended State Space [PDF]

    This chapter reviews my recent attempts to extend the notion of equilibrium entropy to nonequilibrium systems so that it can also capture memory effects. This is done by enlarging the equilibrium state space 𝔖 to 𝔖′ by introducing internal variables. These variables capture the irreversibility due to internal processes. By a proper choice of the enlarged state space 𝔖′, the entropy becomes a state function, which shares many properties of the equilibrium entropy, except for a nonzero irreversible entropy generation. I give both a thermodynamic and a statistical extension of entropy and demonstrate their equivalence in all cases by taking an appropriate 𝔖′. This provides a general non-negative statistical expression of the entropy for any situation.

  • P.D. Gujrati, Overlooked Work and Heat of Intervention and the Fate of Information Principles of Szilard and Landauer, DOI:10.48550/arXiv.2205.02373

    I show that any external intervention (insertion or removal of a partition) that destroys the equilibrium or brings it in a system always requires work and heat to ensure that the first law is obeyed, a fact that has been completely overlooked in literature. Consequently, there is no second law violation. I discuss the ramifications of my finding for information principles of Szilard and Landauer and show that no information entropy is needed. The relevance of this result for Maxwell's demon is also considered.

  • P.D. Gujrati, Maxwell's Conjecture of the Demon creating a Temperature Difference is False, DOI: 10.48550/arXiv.2205.02313

    I argue that Maxwell's demon is incapable of creating a nonzero temperature difference. Hence, it does not destroy equilibrium, and the second law is never at risk, contrary to the claim by Maxwell and accepted by many. It is therefore remarkable that despite this, the demon paradox has been a valuable source of new ideas. I use two independent arguments, one using classical equilibrium thermodynamics by extending Brillouin's approach, and the other one using equilibrium statistical mechanics and the central limit theorem.

  • P.D. Gujrati, The Glass Transition and the Entropy Crisis in Encyclopedia of Glass Science, Technology, History, and Culture, ed. P. Richet, R. Conradt, A. Takada, and J. Dyon, Wiley, Hoboken, USA (2021), https://doi.org/10.1002/9781118801017.ch3.3. See also, The Role of the Communal Entropy and Free Volume for the Viscosity Divergence near the Glass Transition: A New Conceptual Approach, DOI: 10.48550/arXiv.1802.09138.

    The Glass Tranition and the Entropy Crisis [PDF]

    The focus on the "entropy crisis," here is the vanishing of the configurational entropy of a supercooled liquid at a positive temperature TK (Kauzmann temperature). It is shown that this temperature also controls the divergence of viscosity by properly introducing the concept of communal entropy to provide a unified approach to glasses.
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