Reply to the comment of P. Lipavsky

TL;DR

This paper defends the derivation of conservation laws against a critique, clarifying that the critique is based on a mathematical error and confirming the validity of the laws with minor exceptions.

Contribution

The paper refutes a mathematical critique of conservation laws derivation, reaffirming their validity even without the contested relation.

Findings

Conservation laws remain valid despite the critique.

The critique's counterexample is based on an error.

Local entropy terms vanish upon integration.

Abstract

The critics of P. Lipavsky on the derivation of conservation laws including gradient corrections is refuted since his counterexample is based on a mathematical error. Instead, the derived conservation laws for density, momentum and energy remain valid even without using the objected relation. Only for the entropy local terms are missing which vanish under integration.