# Compatibility of linear-response theory with the Second Law of Thermodynamics and the emergence of negative entropy production rates

## TL;DR

This paper examines the compatibility of linear-response theory with the Second Law of Thermodynamics, revealing conditions under which entropy production can be negative, thus challenging traditional assumptions.

## Contribution

It provides a detailed analysis of linear-response theory's consistency with the Second Law, including conditions for positive entropy production and examples of negative rates.

## Key findings

- Linear-response theory aligns with the Second Law for quasistatic processes.
- Finite-time processes can exhibit deviations from expected dissipation.
- Negative entropy production rates can occur in specific nonequilibrium scenarios.

## Abstract

The reliability of physical theories depends on whether they agree with well established physical laws. In this work, we address the compatibility of the Hamiltonian formulation of linear-response theory with the Second Law of Thermodynamics. In order to do so, we verify three complementary aspects often understood as statements of the Second Law: 1. No dissipation for quasistatic process; 2. Dissipation for finite-time processes; 3. Positive entropy production rate. Our analysis focus on two classes of nonequilibrium isothermal processes: slowly-varying and finite-time but weak ones. For the former, we show that these aspects are easily verified. For the later, we present conditions for the achievement of the first two aspects. We also show that the third one is not always verified, presenting an example based on Brownian motion in which we observe negative values in the entropy production rate. In particular, we compare linear-response and exact results for this example.