The second laws of quantum thermodynamics (1305.5278v4)

Abstract: The second law of thermodynamics tells us which state transformations are so statistically unlikely that they are effectively forbidden. Its original formulation, due to Clausius, states that "Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time". The second law applies to systems composed of many particles interacting; however, we are seeing that one can make sense of thermodynamics in the regime where we only have a small number of particles interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are cyclic or very close to cyclic, the second law for microscopic systems takes on a very different form than it does at the macroscopic scale, imposing not just one constraint on what state transformations are possible, but an entire family of constraints. In particular, we find a family of free energies which generalise the traditional one, and show that they can never increase. We further find that there are three regimes which determine which family of second laws govern state transitions, depending on how cyclic the process is. In one regime one can cause an apparent violation of the usual second law, through a process of embezzling work from a large system which remains arbitrarily close to its original state. These second laws are not only relevant for small systems, but also apply to individual macroscopic systems interacting via long-range interactions, which only satisfy the ordinary second law on average. By making precise the definition of thermal operations, the laws of thermodynamics take on a simple form with the first law defining the class of thermal operations, the zeroeth law emerging as a unique condition ensuring the theory is nontrivial, and the remaining laws being a monotonicity property of our generalised free energies.

• The paper establishes that quantum systems require a family of second laws imposing multiple constraints on cyclic or near-cyclic processes.
• It introduces generalized free energies that extend the traditional concept to quantify constraints across distinct quantum regimes.
• The findings offer practical insights for optimizing work extraction and precise state control in quantum computing and nanotechnology.

The Second Laws of Quantum Thermodynamics

This paper, authored by Brandão, Horodecki, ng, Oppenheim, and Wehner, explores an extension of the second law of thermodynamics into the quantum domain, specifically focusing on systems at the microscopic scale. The traditional second law, which constrains the behavior of macroscopic systems, is shown here to present a more complex family of constraints when applied to quantum systems.

Key Contributions

1. Quantum Second Laws: The paper establishes that for cyclic or nearly cyclic processes at the quantum level, there exists a family of second laws, rather than a single law. This set of laws imposes multiple constraints on the transformations of quantum states.
2. Generalized Free Energies: A family of generalized free energies is introduced, each representing a constraint akin to the traditional free energy but applicable to different regimes of quantum thermodynamics. The standard second law is a subset of these constraints.
3. Regimes of Quantum Thermodynamics: Three distinct regimes are identified based on how closely a process approximates cyclic behavior:
   • For certain cyclic processes, it appears as if the traditional second law can be violated. This occurs when work is "embezzled" from a larger system that stays close to its original state.
   • These second laws apply not only to small systems but also to systems with macroscopic properties where only average behavior follows the traditional second law.

Theoretical Implications

• Thermal Operations: The formulation provides a clear division of thermodynamic operations:
  • The first law defines thermal operations involving the conservation of energy.
  • The zeroth law, derived here, sets a unique condition ensuring non-triviality of the theory.
  • The second laws are seen as a monotonicity condition for the generalized free energies.
• Framework for Quantum Thermodynamics: The paper reformulates thermodynamic laws within the quantum framework, aiding in the understanding of energy exchange and state transitions at a more granular level.

Practical Implications

• Work Extraction: These findings have implications for quantum computation and nanotechnology, where exploiting quantum thermodynamic principles could enhance efficiency in energy conversions and computational processes.
• State Transition Criteria: The introduction of generalized free energies can guide the design of quantum systems requiring precise control over state transformations, crucial for quantum simulations and advanced cryptographic systems.

Future Directions

The work paves the way for further research in:

• Quantifying other potential families of thermodynamic laws applicable in various quantum configurations.
• Developing experimental procedures to observe and validate the proposed theoretical constructs.
• Exploring the integration of these principles into quantum computing architectures to harness potential efficiency gains.

In conclusion, this paper expands the landscape of thermodynamics to the quantum scale, providing a robust theoretical framework that challenges classical interpretations and opens new avenues for technological advancement in quantum mechanics and beyond.