Thermodynamics and Legendre Duality in Optimal Networks

Fuente: arXiv
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Main Authors: Porporato, Amilcare, Anand, Shashank Kumar, Calabrese, Salvatore, Ridolfi, Luca, Rondoni, Lamberto
Format: Preprint
Published: 2025
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author Porporato, Amilcare
Anand, Shashank Kumar
Calabrese, Salvatore
Ridolfi, Luca
Rondoni, Lamberto
author_facet Porporato, Amilcare
Anand, Shashank Kumar
Calabrese, Salvatore
Ridolfi, Luca
Rondoni, Lamberto
contents Optimality principles in nonequilibrium transport networks are linked to a thermodynamic formalism based on generalized transport potentials endowed with Legendre duality and related contact structure. This allows quantifying the distance from non-equilibrium operating points, analogously to thermodynamic availability as well as to shed light on optimality principles in relation to different imposed constraints. Extremizations of generalized dissipation and entropy production appear as special cases that require power-law resistances and -- for entropy production -- also isothermal conditions. Changes in stability of multiple operating points are interpreted as phase transitions based on non-equilibrium equations of state, while cost-based optimization of transport properties reveals connections to the generalized dissipation in the case of power law costs and linear resistance law, but now with typically unstable operating points which give rise to branched optimal transport.
format Preprint
id arxiv_https___arxiv_org_abs_2506_15727
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Thermodynamics and Legendre Duality in Optimal Networks
Porporato, Amilcare
Anand, Shashank Kumar
Calabrese, Salvatore
Ridolfi, Luca
Rondoni, Lamberto
Statistical Mechanics
Adaptation and Self-Organizing Systems
Applied Physics
Optimality principles in nonequilibrium transport networks are linked to a thermodynamic formalism based on generalized transport potentials endowed with Legendre duality and related contact structure. This allows quantifying the distance from non-equilibrium operating points, analogously to thermodynamic availability as well as to shed light on optimality principles in relation to different imposed constraints. Extremizations of generalized dissipation and entropy production appear as special cases that require power-law resistances and -- for entropy production -- also isothermal conditions. Changes in stability of multiple operating points are interpreted as phase transitions based on non-equilibrium equations of state, while cost-based optimization of transport properties reveals connections to the generalized dissipation in the case of power law costs and linear resistance law, but now with typically unstable operating points which give rise to branched optimal transport.
title Thermodynamics and Legendre Duality in Optimal Networks
topic Statistical Mechanics
Adaptation and Self-Organizing Systems
Applied Physics
url https://arxiv.org/abs/2506.15727