Making use of the equivalence between information and entropy, we have shown in a recent paper that particles moving with a kinetic energy ε carry potential information i p o t ( ε , T ) = 1 ln ( 2 ) ε k B T relative to a heat reservoir of temperature T . In this paper we build on this result and consider in more detail the process of information gain in photon detection. Considering photons of energy E p h and a photo-ionization detector operated at a temperature T D , we evaluate the signal-to-noise ratio S N ( E p h , T D ) for different detector designs and detector operation conditions and show that the information gain realized upon detection, i r e a l ( E p h , T D ) , always remains smaller than the potential information i p o t ( E p h , T D ) carried with the photons themselves, i.e.,: i r e a l ( E p h , T D ) = 1 ln ( 2 ) ln ( S N ( E p h , T D ) ) ≤ i p o t ( E p h , T D ) = 1 ln ( 2 ) E p h k B T D . This result is shown to be generally valid for all kinds of technical photon detectors, which shows that i p o t ( E p h , T D ) can indeed be regarded as an intrinsic information content that is carried with the photons themselves. Overall, our results suggest that photon detectors perform as thermodynamic engines that incompletely convert potential information into realized information with an efficiency that is limited by the second law of thermodynamics and the Landauer energy bounds on information gain and information erasure.
Making use of the equivalence between information and entropy, we have shown in a recent paper that particles moving with a kinetic energy ε carry potential information i p o t ( ε , T ) = 1 ln ( 2 ) ε k B T relative to a heat reservoir of temperature T . In this paper we build on this result and consider in more detail the process of information gain in photon detection. Considering photons of energy E p h and a photo-ionization detector operated at a temperature T D , we evaluate the signal-to-noise ratio S N ( E p h , T D ) for different detector designs and detector operation conditions and show that the information gain realized upon detection, i r e a l ( E p h , T D ) , always remains smaller than the potential information i p o t ( E p h , T D ) carried with the photons themselves, i.e.,: i r e a l ( E p h , T D ) = 1 ln ( 2 ) ln ( S N ( E p h , T D ) ) ≤ i p o t ( E p h , T D ) = 1 ln ( 2 ) E p h k B T D . This result is shown to be generally valid for all kinds of technical photon detectors, which shows that i p o t ( E p h , T D ) can indeed be regarded as an intrinsic information content that is carried with the photons themselves. Overall, our results suggest that photon detectors perform as thermodynamic engines that incompletely convert potential information into realized information with an efficiency that is limited by the second law of thermodynamics and the Landauer energy bounds on information gain and information erasure.
We review a general theory of thermodynamics of information processing. The background of this topic is the recently-developed nonequilibrium statistical mechanics and quantum (and classical) information theory. These theories are closely related to the modern technologies to manipulate and observe small systems; for example, macromolecules and colloidal particles in the classical regime, and quantum-optical systems and quantum dots in the quantum regime. First, we review a generalization of the second law of thermodynamics to the situations in which small thermodynamic systems are subject to quantum feedback control. The generalized second law is expressed in terms of an inequality that includes the term of information obtained by the measurement, as well as the thermodynamic quantities such as the free energy. This inequality leads to the fundamental upper bound of the work that can be extracted by a “Maxwell's demon”, which can be regarded as a feedback controller with a memory that stores measurement outcomes. Second, we review generalizations of the second law of thermodynamics to the measurement and information erasure processes of the memory of the demon that is a quantum system. The generalized second laws consist of inequalities that identify the lower bounds of the energy costs that are needed for the measurement and the information erasure. The inequality for the erasure leads to the celebrated Landauer's principle for a special case. Moreover, these inequalities enable us to reconcile Maxwell's demon with the second law of thermodynamics. In these inequalities, thermodynamic quantities and information contents are treated on an equal footing. In fact, the inequalities are model-independent, so that they can be applied to a broad class of information processing. Therefore, these inequalities can be called the second law of “information thermodynamics”.
In this paper, we are concerned with the process of experimental information gain. Building on previous work, we show that this is a discontinuous process in which the initiating quantum-mechanical matter-instrument interactions are being turned into macroscopically observable events (EOs). In the course of time, such EOs evolve into spatio-temporal patterns of EOs, which allow conceivable alternatives of physical explanation to be distinguished. Focusing on the specific case of photon detection, we show that during their lifetimes, EOs proceed through the four phases of initiation, detection, erasure and reset. Once generated, the observational value of EOs can be measured in units of the Planck quantum of physical action h=4.136×10-15eVs. Once terminated, each unit of entropy of size kB=8.617×10-5eV/K, which had been created in the instrument during the observational phase, needs to be removed from the instrument to ready it for a new round of photon detection. This withdrawal of entropy takes place at an energetic cost of at least two units of the Landauer minimum energy bound of ELa=ln2kBTD for each unit of entropy of size kB.
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.
Observer-information entropy production quantifies the loss of recoverable information about a physical source when an already formed observation undergoes source-independent irreversible degradation. The statistical second-law statement Σobs[s,t]=I(X;Rs)−I(X;Rt)=I(X;Rs∣Rt)≥0 follows from data processing, but by itself it does not identify a physical energetic or thermodynamic cost. This paper establishes such a connection within an explicit and deliberately restricted stochastic-thermodynamic regime. We consider a finite observer memory Rt coupled to a single heat bath at temperature T. A source label X is fixed during the passive relaxation, the transition generator of Rt is independent of X, and the memory dynamics satisfies detailed balance with respect to a strictly positive equilibrium law q. For the joint source--memory ensemble and for the unconditioned memory marginal, we define the standard stochastic-thermodynamic entropy-production rates. Using the relative-entropy chain rule and the detailed-balance H-theorem, we prove the exact correlation-dissipation decomposition kBS˙totXR=σobs+kBS˙totR. Consequently, S˙totXR≥kBσobs,ΔStotXR[s,t]≥kBΣobs[s,t]. At fixed temperature the same result is an excess-free-energy dissipation bound, \[ \Fex_{XR}(s)-\Fex_{XR}(t) \ge k_BT\Sigma_{\mathrm{obs}}[s,t]. \] Equality holds when the memory marginal remains at equilibrium, in which case all thermodynamic irreversibility is attributable to the destruction of source--record correlation. A symmetric two-state memory provides an exactly solvable saturation example. The result is not a universal Landauer principle. It constrains total entropy production and loss of nonequilibrium free energy during passive decorrelation; it does not assert a universal heat or work cost for arbitrary information loss. Driven memories, source-dependent transition rates, active measurement, feedback, multiple reservoirs, and nonequilibrium steady states require the broader information-thermodynamic bookkeeping developed in stochastic thermodynamics. We then place the thermodynamic result beside two Fisher--Shannon bridges. Under Gaussian observation heat flow Yt=X+Bt, observer-information dissipation obeys the exact identity σobs(t)=21(td−J(Yt))=2t21mmse(X∣Yt), while pairwise statistical distinguishability obeys \[ \frac{d}{dt}\KL(p_t\|q_t) =-\frac12\Jrel(p_t\|q_t). \] Recent temporal-Fisher speed-limit results provide a complementary route from physical entropy production to the speed of probability evolution. Together these results separate three objects that are often conflated: thermodynamic irreversibility, Shannon information loss about the physical source, and Fisher-geometric statistical motion. The paper thereby supplies a physical-cost layer for observer information theory without identifying information with energy or thermodynamic entropy.