Abstract We frame Newton’s Law of Cooling as a gradient flow within the context information geometry. This connects it to thermodynamic uncertainty relation and Horse-Carrot Theorem, reveals novel instances asymmetric relaxations in endoreversible processes. present general criterion for predicting asymmetries using Amari-Chentsov tensor, applicable classical quantum thermodynamics. Examples include faster cooling ideal gases akin Mpemba effect gases.

We use a formulation of Noether's theorem for contact Hamiltonian systems to derive relation between the thermodynamic entropy and Noether invariant associated with time-translational symmetry. In particular case thermostatted at equilibrium, we show that total system plus reservoir are conserved as consequence thereof. Our results contribute understanding from geometric point view.

In this paper we show that the vanishing of scalar curvature Ruppeiner-like metrics does not characterize ideal gas. Furthermore, claim through an example flatness is a sufficient condition to establish absence interactions in underlying microscopic model thermodynamic system, which poses limitation on usefulness Ruppeiner’s metric and conjecture. Finally, address problem choice coordinates black hole thermodynamics. We propose alternative energy representation for Kerr-Newman holes mimics...

We present a rigorous mathematical treatment of Ruppeiner geometry, by considering degenerate Hessian metrics defined on radiant manifolds. A manifold [Formula: see text] is said to be if it endowed with symmetric, flat connection and global vector field whose covariant derivative the identity mapping. metric tensor that can locally written as function, called potential. function extensive its Lie respect itself. show appearing in equilibrium thermodynamics are necessarily degenerate, owing...

We introduce a novel perspective on Newton's Law of Cooling by framing it within the context information geometry. By characterizing as specific representation gradient flow, we establish connection with well-known Horse-Carrot Theorem and reveal previously unexplored instances asymmetric relaxations in endoreversible processes. present completely general practical criterion for predicting asymmetries based Amari-Chentsov tensor, whose applicability extends to both classical quantum...

This paper presents a rigorous treatment of the concept extensivity in equilibrium thermodynamics from geometric point view.This is achieved by endowing manifold states system with smooth atlas that compatible pseudogroup transformations on vector space preserve radial field.The resulting structure allows for accurate definitions extensive differential forms and scaling, well-known relationship between both reproduced.This represented global field locally written as one.The submanifolds are...

We derive a formula for the dry adiabatic lapse rate of atmospheres composed real gases. restrict our study to those described by family two-parameter cubic equations state and recent Guevara non-cubic equation. Since depends on curves, we compute them all at once, considering molecules that can move, rotate, vibrate, any equation state. To illustrate results, estimate troposphere Titan, obtaining better approximation observed data in some instances, when compared estimation provided virial...