# Nonlinear refrigerator with a finite-sized cold heat bath

## TL;DR

This paper analyzes a nonlinear refrigerator operating between a finite cold heat bath and an infinite hot heat bath, deriving optimal temperature paths and performance bounds in the nonlinear response regime.

## Contribution

It introduces a model for a nonlinear refrigerator with a finite cold bath, deriving optimal temperature change paths and performance bounds considering asymmetric dissipation.

## Key findings

- Derived optimal temperature change path minimizing input work.
- Calculated coefficient of performance as a function of input power.
- Established bounds for the coefficient of performance under dissipation limits.

## Abstract

We study the refrigerator working between a finite-sized cold heat bath and an infinite-sized hot heat bath (environment) in the nonlinear response regime. We assume that the initial temperature $T_i$ of the finite-sized cold heat bath satisfies $T_i\leq T_h$, where $T_h$ is the temperature of the hot heat bath. By consuming the input power, the refrigerator transfers the heat from a finite-sized cold heat bath to the hot heat bath. Hence, the temperature of the finite-sized cold heat bath decreases until it reaches the desired low-temperature $T_f$. By minimizing the input work for the heat transport process, we derive the optimal path for temperature change. We calculate the coefficient of performance as a function of average input power. We also obtain the bounds for the coefficient of performance by applying the asymmetric dissipation limits.