The behavior of systems near critical points is a long-standing puzzle in statistical mechanics and solid-state physics. Experimentally this behavior is characterized by divergences in a variety of thermodynamic quantities as powers of the deviation from criticality. These divergences are described by critical indices, which are the exponents in power laws; for example, the susceptibility of a ferromagnet diverges like (T−Tc)γ as T approaches Tc.
The behavior of systems near critical points is a long-standing puzzle in statistical mechanics and solid-state physics. Experimentally this behavior is characterized by divergences in a variety of thermodynamic quantities as powers of the deviation from criticality. These divergences are described by critical indices, which are the exponents in power laws; for example, the susceptibility of a ferromagnet diverges like (T−Tc)γ as T approaches Tc.
We describe a new approach to the understanding of the thermodynamic properties of a physical system near a critical point. The critical point is characterized by the peculiar dependence of various quantities on the size of the system, rather than by the mathematical singularities which appear in an infinite system. We indicate a very general method of obtaining scaling laws for the critical behavior of any thermodynamic system by considering its thermodynamic fluctuations. As an example, a new scaling law is obtained for the susceptibility at a gas-liquid critical point.
Phase transitions represent fundamental transformations of matter, characterized by abrupt changes in macroscopic properties and often associated with singular behavior at critical points. While equilibrium aspects of phase transitions, particularly universal critical exponents and scaling laws, are well-understood, the non-equilibrium processes occurring near criticality, especially the production of entropy, remain a rich area of investigation. This paper explores the intricate relationship between critical entropy production and the emergence of scaling laws in systems undergoing phase transitions. We delve into how the rate of entropy production diverges or exhibits anomalous scaling near critical points, reflecting the system's attempts to dissipate energy and respond to external perturbations as it approaches a state of macroscopic change. By integrating concepts from non-equilibrium thermodynamics, statistical mechanics, and renormalization group theory, we aim to elucidate the underlying mechanisms that govern entropy generation in these critical regimes. We discuss theoretical frameworks that predict universal scaling behaviors for entropy production rates, analogous to those observed for equilibrium order parameters and susceptibilities. The implications of these scaling laws extend beyond theoretical physics, offering insights into complex systems, far-from-equilibrium dynamics, and the efficiency of energy conversion processes in critical environments. Our analysis highlights the critical entropy production as a unique signature of non-equilibrium dynamics during phase transitions, providing a deeper understanding of the interplay between fluctuations, dissipation, and universality near points of instability.
Abstract In this chapter we introduce some general concepts of statistical mechanics and phase transitions, in order to give a rapid overview of the different topics of the subject and their physical relevance. For the sake of clarity and simplicity, we will focus our attention on magnetic systems but it should be stressed that the concepts discussed here are of a more general nature and can be applied to other systems as well. We will analyze, in particular, the significant role played by the correlation length in the phase transitions and the important properties of universality observed in those phenomena. As we will see, near a phase transition the thermodynamic quantities of a system present an anomalous power law behavior, parameterized by a set of critical exponents.
By the early 1960's advances in statistical physics had established the existence of universality classes for systems with second-order phase transitions and characterized these by critical exponents which are different to the classical ones. There followed the discovery of (now famous) scaling relations between the power-law critical exponents describing second-order criticality. These scaling relations are of fundamental importance and now form a cornerstone of statistical mechanics. In certain circumstances, such scaling behaviour is modified by multiplicative logarithmic corrections. These are also characterized by critical exponents, analogous to the standard ones. Recently scaling relations between these logarithmic exponents have been established. Here, the theories associated with these advances are presented and expanded and the status of investigations into logarithmic corrections in a variety of models is reviewed.
By the early 1960's advances in statistical physics had established the existence of universality classes for systems with second-order phase transitions and characterized these by critical exponents which are different to the classical ones. There followed the discovery of (now famous) scaling relations between the power-law critical exponents describing second-order criticality. These scaling relations are of fundamental importance and now form a cornerstone of statistical mechanics. In certain circumstances, such scaling behaviour is modified by multiplicative logarithmic corrections. These are also characterized by critical exponents, analogous to the standard ones. Recently scaling relations between these logarithmic exponents have been established. Here, the theories associated with these advances are presented and expanded and the status of investigations into logarithmic corrections in a variety of models is reviewed.
Critical phenomena, characterized by abrupt changes in the macroscopic properties of a system, exhibit a profound degree of universality, meaning that vastly different physical systems can display identical behavior near their critical points. This universality is typically understood through the lens of scaling laws and the Renormalization Group theory, which classify critical points into distinct universality classes. This paper proposes and explores the "Entropic Law of Critical Universality," an overarching principle positing that not only do thermodynamic quantities scale universally, but the fundamental information-theoretic measures of a system, particularly entropy in its various forms (thermodynamic entropy, entanglement entropy, Renyi entropy), also conform to universal scaling behaviors that uniquely characterize these universality classes. We review how entanglement entropy exhibits universal logarithmic corrections at quantum critical points, linked to the central charge of underlying conformal field theories. We also discuss how specific entropy behaves non-monotonically near quantum chromodynamics critical points and how entropic measures can identify phase transitions and their classes in various condensed matter systems, including graphene and spin models. The paper synthesizes theoretical frameworks and empirical evidence to demonstrate that entropy serves as a powerful and often more direct probe of the universal properties underlying critical phenomena, offering a comprehensive perspective on the shared information landscape of diverse critical systems.