We discuss some features of thermodynamics in the presence of multiple conserved quantities.We prove a generalisation of Landauer principle illustrating tradeoffs between the erasure costs paid in different 'currencies'.We then show how the maximum entropy and complete passivity approaches give different answers in the presence of multiple observables.We discuss how this seems to prevent current resource theories from fully capturing thermodynamic aspects of non-commutativity.
We discuss some features of thermodynamics in the presence of multiple conserved quantities.We prove a generalisation of Landauer principle illustrating tradeoffs between the erasure costs paid in different 'currencies'.We then show how the maximum entropy and complete passivity approaches give different answers in the presence of multiple observables.We discuss how this seems to prevent current resource theories from fully capturing thermodynamic aspects of non-commutativity.
In this chapter we address the topic of quantum thermodynamics in the presence of additional observables beyond the energy of the system. In particular we discuss the special role that the generalized Gibbs ensemble plays in this theory, and derive this state from the perspectives of a micro-canonical ensemble, dynamical typicality and a resource-theory formulation. A notable obstacle occurs when some of the observables do not commute, and so it is impossible for the observables to simultaneously take on sharp microscopic values. We show how this can be circumvented, discuss information-theoretic aspects of the setting, and explain how thermodynamic costs can be traded between the different observables. Finally, we discuss open problems and future directions for the topic.
We extend the tools of quantum resource theories to scenarios in which multiple quantities (or resources) are present, and their interplay governs the evolution of physical systems. We derive conditions for the interconversion of these resources, which generalise the first law of thermodynamics. We study reversibility conditions for multi-resource theories, and find that the relative entropy distances from the invariant sets of the theory play a fundamental role in the quantification of the resources. The first law for general multi-resource theories is a single relation which links the change in the properties of the system during a state transformation and the weighted sum of the resources exchanged. In fact, this law can be seen as relating the change in the relative entropy from different sets of states. In contrast to typical single-resource theories, the notion of free states and invariant sets of states become distinct in light of multiple constraints. Additionally, generalisations of the Helmholtz free energy, and of adiabatic and isothermal transformations, emerge. We thus have a set of laws for general quantum resource theories, which generalise the laws of thermodynamics. We first test this approach on thermodynamics with multiple conservation laws, and then apply it to the theory of local operations under energetic restrictions.
We extend the tools of quantum resource theories to scenarios in which multiple quantities (or resources) are present, and their interplay governs the evolution of physical systems. We derive conditions for the interconversion of these resources, which generalise the first law of thermodynamics. We study reversibility conditions for multi-resource theories, and find that the relative entropy distances from the invariant sets of the theory play a fundamental role in the quantification of the resources. The first law for general multi-resource theories is a single relation which links the change in the properties of the system during a state transformation and the weighted sum of the resources exchanged. In fact, this law can be seen as relating the change in the relative entropy from different sets of states. In contrast to typical single-resource theories, the notion of free states and invariant sets of states become distinct in light of multiple constraints. Additionally, generalisations of the Helmholtz free energy, and of adiabatic and isothermal transformations, emerge. We thus have a set of laws for general quantum resource theories, which generalise the laws of thermodynamics. We first test this approach on thermodynamics with multiple conservation laws, and then apply it to the theory of local operations under energetic restrictions.
Thermodynamics and information have intricate interrelations. Often thermodynamics is considered to be the logical premise to justify that information is physical - through Landauer's principle -, thereby also linking information and thermodynamics. This approach towards information has been instrumental to understand thermodynamics of logical and physical processes, both in the classical and quantum domain. In the present work, we formulate thermodynamics as an exclusive consequence of information conservation. The framework can be applied to the most general situations, beyond the traditional assumptions in thermodynamics: we allow systems and thermal baths to be quantum, of arbitrary sizes and even possessing inter-system correlations.Here, systems and baths are not treated differently, rather both are considered on an equal footing. This leads us to introduce a ''temperature''-independent formulation of thermodynamics. We rely on the fact that, for a fixed amount of information, measured by the von Neumann entropy, any system can be transformed to a state with the same entropy that possesses minimal energy. This state, known as a completely passive state, acquires Boltzmann-Gibbs canonical form with an intrinsic temperature . We introduce the notions of bound and free energy and use them to quantify heat and work, respectively. Guided by the principle of information conservation, we develop universal notions of equilibrium, heat and work, Landauer's principle and universal fundamental laws of thermodynamics. We demonstrate that the maximum efficiency of a quantum engine with a finite bath is in general lower than that of an ideal Carnot engine. We introduce a resource theoretic framework for our intrinsic temperature based thermodynamics, within which we address the problem of work extraction and state transformations. Finally, the framework is extended to multiple conserved quantities.
Thermodynamics and information have intricate interrelations. Often thermodynamics is considered to be the logical premise to justify that information is physical - through Landauer's principle -, thereby also linking information and thermodynamics. This approach towards information has been instrumental to understand thermodynamics of logical and physical processes, both in the classical and quantum domain. In the present work, we formulate thermodynamics as an exclusive consequence of information conservation. The framework can be applied to the most general situations, beyond the traditional assumptions in thermodynamics: we allow systems and thermal baths to be quantum, of arbitrary sizes and even possessing inter-system correlations.Here, systems and baths are not treated differently, rather both are considered on an equal footing. This leads us to introduce a ''temperature''-independent formulation of thermodynamics. We rely on the fact that, for a fixed amount of information, measured by the von Neumann entropy, any system can be transformed to a state with the same entropy that possesses minimal energy. This state, known as a completely passive state, acquires Boltzmann-Gibbs canonical form with an intrinsic temperature. We introduce the notions of bound and free energy and use them to quantify heat and work, respectively. Guided by the principle of information conservation, we develop universal notions of equilibrium, heat and work, Landauer's principle and universal fundamental laws of thermodynamics. We demonstrate that the maximum efficiency of a quantum engine with a finite bath is in general lower than that of an ideal Carnot engine. We introduce a resource theoretic framework for our intrinsic temperature based thermodynamics, within which we address the problem of work extraction and state transformations. Finally, the framework is extended to multiple conserved quantities.
The Landauer's principle, a cornerstone of information thermodynamics, provides a fundamental lower bound on the energetic cost of information erasure in terms of the information content change. However, its traditional formulation is largely confined to systems exchanging solely energy with an ideal thermal bath. In this work, we derive general information-cost trade-off relations that go beyond the scope of Landauer's principle by developing a thermodynamic inference approach based on the maximum entropy principle. These relations require only information about the system and are applicable to complex quantum scenarios involving multiple conserved charges and non-thermal environments. Specifically, we present two key results: (i) In scenarios where only the mean values of observables are accessible, we derive an information-content-informed upper bound on the thermodynamic cost which complements an existing generalized Landauer lower bound. (ii) When second-order fluctuations can also be measured, we obtain an information-content-informed lower bound on the change in variances of observables, thereby extending the Landauer's principle to constrain higher-order fluctuation costs. We numerically validate our information-cost trade-off relations using a coupled-qubit system exchanging energy and excitations, a driven qubit implementing an information erasure process, and a driven double quantum dot system that can operate as an inelastic heat engine. Our results underscore the broad utility of maximum-entropy inference in constraining thermodynamic costs for generic finite-time quantum processes, with direct relevance to quantum information processing and quantum thermodynamic applications.