# Variational principles and thermodynamics

## TL;DR

This paper explores the limitations of traditional variational principles in dissipative systems and proposes using the second law of thermodynamics as a more effective tool for deriving evolution equations.

## Contribution

It demonstrates that the second law can be used to construct evolution equations for both dissipative and nondissipative systems, offering an alternative to variational principles.

## Key findings

- Variational principles are limited for dissipative systems.
- Thermodynamics can reproduce ideal process equations.
- The second law alone can guide the derivation of evolution equations.

## Abstract

Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With methods of modern nonequilibrium thermodynamics, one can derive evolution equations for dissipative phenomena and, surprisingly, can also reproduce the Euler-Lagrange form of the evolution equations for ideal processes. In this work, we examine some demonstrative examples and compare thermodynamic and variational techniques. Then, we argue that instead of searching for variational principles for dissipative systems, a different program can be more fruitful: the second law alone can be an effective tool to construct both dissipative and nondissipative evolution equations.