# Unified first law for traversable wormholes in non-minimal coupling of curvature and matter

## TL;DR

This paper explores the thermodynamics of static Morris-Thorne wormholes within $f(R)$ gravity, focusing on non-minimal curvature-matter coupling, and generalizes previous Einstein gravity results.

## Contribution

It introduces a generalized thermodynamic framework for wormholes in $f(R)$ gravity with curvature-matter coupling, extending prior Einstein gravity findings.

## Key findings

- Generalized surface gravity and thermodynamics at wormhole horizons.
- Derived complex equations for non-minimal curvature-matter coupling.
- Extended thermodynamic laws to modified gravity scenarios.

## Abstract

In this paper thermodynamics of static Morris-Thorne wormholes has been discussed in the context of $f(R)$ gravity. The generalized surface gravity, unified first law of thermodynamics and wormhole dynamics have been studied at trapping horizons. We have investigated thermodynamics in non-minimal coupling of curvature and matter which produces very complex equations. Our results generalize the results that have already been derived in Einstein's gravity in the absence of curvature-matter coupling.