Thermodynamics as a Consequence of Information Conservation

In this work we formulate thermodynamics as an exclusive consequence of information conservation. The framework can be applied to most general situations, beyond the traditional assumptions in thermodynamics, where systems and thermal-baths could be quantum, of arbitrary sizes and even could posses inter-system correlations. Further, it does not require a priory predetermined temperature associated to a thermal-bath, which does not carry much sense for finite-size cases. Importantly, the thermal-baths and systems are not treated here differently, rather both are considered on equal footing. This leads us to introduce a "temperature"-independent formulation of thermodynamics. We rely on the fact that, for a given amount of information, measured by the von Neumann entropy, any system can be transformed to a state that possesses minimal energy. This state is known as a completely passive state that acquires a Boltzmann--Gibb's canonical form with an intrinsic temperature. We introduce the notions of bound and free energy and use them to quantify heat and work respectively. We explicitly use the information conservation as the fundamental principle of nature, and develop universal notions of equilibrium, heat and work, universal fundamental laws of thermodynamics, and Landauer's principle that connects thermodynamics and information. We demonstrate that the maximum efficiency of a quantum engine with a finite bath is in general different and smaller than that of an ideal Carnot's engine. We introduce a resource theoretic framework for our intrinsic-temperature based thermodynamics, within which we address the problem of work extraction and inter-state transformations. We also extend the framework to the cases of multiple conserved quantities.