Generalized Clausius relation and power dissipation in non equilibrium stochastic systems

Abstract

We extend certain basic and general concepts of thermodynamics to discrete Markov systems exchanging work and heat with reservoirs. In this framework we show that the celebrated Clausius inequality can be generalized and becomes an equality, significantly extending several recent results. We further show that achieving zero dissipation in a system implies that detailed balance obtains, and as a consequence there is zero power production. We obtain inequalities for power production under more general circumstances and show that near equilibrium obtaining maximum power production requires dissipation to be of the same order of magnitude.

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• Free energy and entropy production rate for a Brownian particle that walks on overdamped medium
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• Exact time-dependent analytical solutions for entropy production rate for a system that operates in a heat bath where its temperature varies linearly in space
• Effect of viscous friction on entropy, entropy production and entropy extraction rates in underdamped and overdamped media