# Jensen Inequality and the Second Law

## TL;DR

This paper critically examines the use of Jensen's Inequality in microscopic thermodynamics, revealing potential misconceptions about its role in establishing the second law.

## Contribution

It challenges the common reliance on Jensen's Inequality for proving the second law's consistency in fluctuation theorems, highlighting possible limitations.

## Key findings

- Jensen's Inequality may be misleading in certain thermodynamic contexts
- The paper questions the universal applicability of Jensen's Inequality in fluctuation theorems
- Provides a critical perspective on the foundational tools used in microscopic thermodynamics

## Abstract

Jensen's Inequality (JIEQ) has proved to be a major tool to prove the consistency of various fluctuation theorems with the second law in microscopic thermodynamics. We show that the situation is far from clear and the reliance on the JIE may be quite misleading in general.