Search Talks

Legendre transform between thermodynamic quantities such as the Helmholtz free energy and entropy plays a key role in the formulation of the canonical ensemble. In the standard treatment, the transform exchanges the independent variable from the system’s internal energy to its conjugate variable—the inverse temperature of the heat reservoir. In this article, we formulate a microscopic version of the trans- form between the free energy and Shannon entropy of the system, where the conju- gate variables are the microstate probabilities and the energies (scaled by the inverse temperature). The present approach gives a non-conventional perspective on the connection between information-theoretic measure of entropy and thermodynamic entropy. We focus on the exact differential property of Shannon entropy, utilizing it to derive central relations within the canonical ensemble. Thermodynamics of a system in contact with the heat reservoir is discussed in this framework. Other approaches, in particular, Jaynes’ maximum entropy principle is compared with the present approach. Ref: R.S. Johal, Microscopic Legendre Transform, Canonical Ensemble and Jaynes’ Maximum Entropy Principle, Foundations of Physics, 55:12 (2025). https://doi.org/10.1007/s10701-025-00824-7

Motility-induced phase separation (MIPS) describes how self-propelling particles phase-separate due to their motility, a phenomenon observed in many natural systems. Many motile organisms thrive in fluid environments, and chaotic background flows often act as mixing agents. This raises the question: how does background flow affect the phase separation of motile organisms? To explore this, we study active Brownian particles (ABPs) in a periodic four-roll-mill flow using numerical simulations. Without flow, the system undergoes MIPS. We maintain a packing fraction of 0.7 and investigate the effect of flow on phase separation, referred to as flow-induced phase separation (FIPS). To probe the FIPS regime, we define an order parameter that provides clear insights into this type of phase separation. Additionally, we explore the FIPS region by varying the Peclet number (Pe) and packing fraction (ϕ), which enhances our understanding of how these factors influence the phase separation dynamics.

We study extreme events of avalanche activities in finite-size two-dimensional self- organized critical (SOC) models, specifically the stochastic Manna model (SMM) and Bak-Tang-Weisenfeld (BTW) sandpile model. Employing the approach of block maxima, the study numerically reveals that the distributions for extreme avalanche size and area follow the generalized extreme value (GEV) distribution. The extreme avalanche size follows the Gumbel distribution with shape parameter $\xi=0$ while in case of the extreme avalanche area, we report $\xi>0$. We propose scaling functions for extreme avalanche activities that connect the activities on different length scales. With the help of data collapse, we estimate the precise values of these critical exponents. The scaling functions provide an understanding of the intricate dynamics for different variants of the sandpile model, shedding light on the relationship between system size and extreme event characteristics. Our findings give insight into the extreme behavior of SOC models and offer a framework to understand the statistical properties of extreme events.

We introduce a new class of first passage time optimization mediated by a threshold resetting (TR) mechanism. Inspired by many natural processes that operate under “safety covenant” or are governed by “threshold triggered events” wherein a system, structure, or process exceeds a predefined limit (threshold), causing failure, degradation, or a transition to a different state; we consider an arbitrary first passage process that is intermittently renewed when the search agents, looking for targets, are simultaneously reset upon reaching a certain threshold. Unlike the classical paradigm where the resetting events are externally modulated, here they are event driven and thus, strongly coupled to the system variables. Furthermore, the simultaneous resetting induces long-range interactions between the searchers. A unified theoretical framework is presented for computing the search time associated with this class of correlated stochastic processes, further showcasing a rich and diverse optimization phenomena.