# Stochastic and Quantum Thermodynamics of Driven RLC Networks

## TL;DR

This paper develops a comprehensive stochastic thermodynamics framework for driven RLC networks, incorporating topology, nonisothermal conditions, and quantum effects, enabling the design of circuit-based thermal machines.

## Contribution

It introduces a novel thermodynamics theory for complex RLC networks, including quantum effects and exact energy current formulas under time-dependent driving.

## Key findings

- Designed a circuit-based refrigerator as an example application.
- Derived exact low-temperature quantum results for electrical noise.
- Generalized the Landauer-Buttiker formula for energy currents with driving protocols.

## Abstract

We develop a general stochastic thermodynamics of RLC electrical networks built on top of a graph-theoretical representation of the dynamics commonly used by engineers. The network is: open, as it contains resistors and current and voltage sources, nonisothermal as resistors may be at different temperatures, and driven, as circuit elements may be subjected to external parametric driving. The proper description of the heat dissipated in each resistor requires care within the white noise idealization as it depends on the network topology. Our theory provides the basis to design circuits-based thermal machines, as we illustrate by designing a refrigerator using a simple driven circuit. We also derive exact results for the low temperature regime in which the quantum nature of the electrical noise must be taken into account. We do so using a semiclassical approach which can be shown to coincide with a fully quantum treatment of linear circuits for which canonical quantization is possible. We use it to generalize the Landauer-Buttiker formula for energy currents to arbitrary time-dependent driving protocols.