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An absorption edge is an abrupt change in photon absorption as incident photon energy crosses an electronic excitation threshold. For inner-shell photoionization, a new vacancy-production channel opens near the shell's binding energy. This threshold concerns incident energy; a Characteristic X-ray concerns a subsequent difference of atomic energies. They are different observations. Barkla's lecture explicitly treats characteristic emission as requiring a critical excitation condition, while discussing characteristic radiation separately from scattering.^[ref]

In the stipulated X-ray fluorescence model, the K threshold is $10.0\mathrm{keV}$, whereas the K lines are $8.5$ and $9.7\mathrm{keV}$. An absorber made of a different material could have its own absorption edge between those line energies, preferentially removing the upper line. Actual near-edge structure and attenuation values require material data; the following deliberately chosen coefficients are not such data.

A concrete quantum quench experiment loaded a Bose-Einstein condensate of ${}^{87}\mathrm{Rb}$ chemical atoms from a magnetic field trap into an optical lattice: three orthogonal $838\mathrm{nm}$ laser standing waves, with approximately $125\mu \mathrm{m}$ beam waists. An $80\mathrm{ms}$ loading ramp preceded a $50\mu \mathrm{s}$ increase in lattice depth. This suppressed quantum tunnelling while retaining each well's vibrational ground state. The switch preserved atom-number populations rather than freezing every motional degree of freedom.^[ref]

After variable hold times, releasing the traps and taking photon absorption images after $16\mathrm{ms}$ of flight revealed disappearance and return of interference peaks. Background-subtracted peak counts supplied a coherent fraction. Varying final depth tested the predicted revival period $h/U$; varying initial depth tested the collapse's sensitivity to atom-number statistics. Peak broadening outside counting windows and spatial variation of $U$ limited later signals.^[ref]

Here $U$ is the on-site interaction energy. The approximate isolated-well Hamiltonian operator $H=U\hat{n}(\hat{n}-1)/2$, with number operator $\hat{n}$, gives different quantum phases to its number states, which later rephase. This is a many-level realization of the distinction between fixed populations and changing quantum phases.^[ref]

Take a single isolated optical transition of angular frequency ${\omega }_0$. Both beams have laboratory angular frequency ${\omega }_L$, with laser detuning $\delta ={\omega }_L-{\omega }_0$. Let the pump travel along $+z$, the probe along $-z$, $v$ denote an atom's $z$-velocity, and $k={\omega }_0/c$ be the approximate vacuum wavenumber; $c$ is the speed of light. To first order in $v/c$, the laser detunings in the atom's frame areThe pump addresses atoms near $v=\delta /k$, while the probe addresses atoms near $v=-\delta /k$. For the same transition, simultaneous exact resonance requires both expressions to vanish: adding and subtracting gives $\delta =0$ and $v=0$. The selected atoms can still have substantial transverse velocity. Finite natural linewidth admits a narrow interval of longitudinal velocities; a warm gas has not been cooled.

This is velocity selection, not cancellation of each atom's Doppler shift within a single absorption event. Changing laser detuning selects different atoms for ordinary photon absorption, but only near line centre do these two selected classes overlap. Laser cooling instead changes the distribution of the atoms' velocities through repeated momentum transfer.

Consider equal opposing laser beams along the $x$ axis and an atom with velocity $v$. Let ${\omega }_L$ be their angular frequency, ${\omega }_0$ the atomic resonance angular frequency, $k=2\pi /\lambda >0$ their wavenumber, and $\delta ={\omega }_L-{\omega }_0$ the laser detuning. Red detuning means $\delta <0$. To first order in $v/c$, the atom seesFor small positive $v$, the beam travelling towards negative $x$ is closer to resonance and causes more photon absorption; its momentum kicks point against $v$. The beam travelling towards positive $x$ is further from resonance. Reversing $v$ exchanges the roles of the two beams. This is a Doppler effect on the absorption rates, rather than a need to follow each atom with a moving beam.

An absorbed photon gives the atom momentum $\pm \hslash k$, where $\hslash =h/(2\pi )$ is the reduced Planck constant. Subsequent spontaneous emission gives a recoil opposite to the emitted photon. For an emission pattern symmetric under reversal of direction, that recoil has zero expected value, but nonzero variance. Its mean therefore leaves the directional absorption force intact, while its randomness adds recoil energy. Random absorption times and choices of beam add further momentum fluctuations. Zero mean recoil does not mean zero heating.

For the ideal Wannier-Mott exciton in energy bands whose edges occur at the same crystal momentum, the pair excitation energy, measured from the unexcited crystal, isHere $\hslash \mathbf{K}$ is the pair's total crystal momentum; the last term is center of mass kinetic energy. For a permitted photon absorption transition with negligible recoil energy, $\hslash \omega \simeq E_g-E_{B,n}$. An electric-dipole selection rule and a nonzero transition matrix element are still needed: a bound state need not produce an observable spectral line. If the relevant energy band edges have different values of crystal momentum, a phonon can also be needed to conserve crystal momentum; subtracting a binding scale from a band gap alone does not specify the optical threshold.

For example, the lowest internal bound state in this hypothetical model costs $1.489115\mathrm{eV}$ to create optically, yet needs only $0.010885\mathrm{eV}$ more to dissociate. The large creation energy and the small exciton binding energy answer different physical questions. An electron-hole recombination event can instead release excitation energy by photon emission or to other degrees of freedom; an emitted photon need not reproduce the original absorption energy if relaxation intervened.

Fluorescence is photon emission following photon absorption by matter: an excited state releases some of its energy as light. A fluorophore can therefore mark where something is, while its fluorescence emission spectrum and fluorescence lifetime report different aspects of its environment. Fluorescein is one example; FRET exploits a competing route for excitation energy rather than requiring a second emitted photon.

The usual molecular sequence is excitation, relaxation, then emission, as in the Jablonski diagram. The emitted photon commonly has lower energy and longer wavelength, giving a Stokes shift; the exceptions are discussed below.^[ref]

Infrared is electromagnetic radiation with wavelengths longer than the red end of ordinarily visible light. A useful named convention is the CIE range $780\mathrm{nm}$ to $1\mathrm{mm}$; the approximate visible range $400$–$700\mathrm{nm}$ used in some teaching texts puts the boundary nearer $700\mathrm{nm}$. ^[ref]. Neither number is a sharp physical cutoff of human vision. The CIE divisions IR-A, IR-B and IR-C are respectively $0.78$–$1.4\mu \mathrm{m}$, $1.4$–$3\mu \mathrm{m}$ and $3$–$1000\mu \mathrm{m}$; the boundaries of near-, middle- and far-infrared vary between applications. ^[ref].

Use vacuum wavelength $\lambda$ when comparing these ranges. With frequency $\nu$, speed of light $c$, Planck constant $h$ and photon energy $E$,Thus the CIE infrared interval corresponds approximately to $3.00\times 10^{11}$–$3.84\times 10^{14}\mathrm{Hz}$ and $1.99\times 10^{-22}$–$2.55\times 10^{-19}\mathrm{J}$ per photon, with the smaller energy at the longer wavelength. A $940\mathrm{nm}$ infrared photon has $E\simeq 2.11\times 10^{-19}\mathrm{J}$, whereas a $254\mathrm{nm}$ ultraviolet photon has $E\simeq 7.82\times 10^{-19}\mathrm{J}$. These are calculations from $hc/\lambda$, not measurements of a particular source. A television remote is a familiar approximately $940\mathrm{nm}$ source; its information is carried by variations in the emitted radiant flux. ^[ref].

Detection and visual perception answer different questions. A photodetector can respond to infrared even when an observer perceives no light; a thermometer detects an increase in temperature after photon absorption. Conversely, a small readout can reflect a small spectral responsivity, rather than absence of incident electromagnetic radiation. Images made from infrared readouts use display colors chosen by the imaging system; those colors are not the colors of the incoming infrared.

The important microscopic mechanisms also differ. In infrared spectroscopy, photon absorption often increases the energy of a normal mode in which chemical bonds stretch or bend. The corresponding optical spectrum helps distinguish molecules by their motions. For the usual electric dipole mechanism, the motion must change the electric dipole moment; matching the frequency alone is not sufficient. ^[ref]. Electronic processes can also emit or absorb infrared, so it is not exclusively radiation from molecular motion. ^[ref]; ^[ref].

Infrared is especially useful for observing thermal radiation from objects near everyday temperatures. For an ideal $300\mathrm{K}$ blackbody, Wien's displacement law gives a wavelength peak near $9.66\mu \mathrm{m}$. A thermal camera's readout nevertheless depends on emissivity, reflected surroundings and transmission along the path, as well as temperature. ^[ref]. A source emitting infrared need not be hot: an infrared remote is useful precisely because a photodetector can distinguish its signal from a background. Visible light and ultraviolet can also cause heating when absorbed; “infrared” names a wavelength range, not a unique form of heat.

Herschel's 1800 discovery made the distinction between sight and detection experimentally concrete. His report describes a optical prism spreading sunlight across a white, ruled receiving surface, with three thermometers at different positions near the end of the visible optical spectrum. He observed heating beyond the red edge where no visible color appeared. The result established that sunlight contained invisible radiation less strongly refracted by that optical prism than the visible red; it did not measure a photon energy or establish today's infrared boundaries. ^[ref]; ^[ref].

A documented modern version by Caltech/IPAC uses a glass optical prism, white paper in a shaded box and three blackened liquid-filled thermometers. Initial readings in shade provide each thermometer's baseline; subsequent readings compare blue, yellow and just beyond red after the bulbs have had time to warm. The measured quantity is the rise in temperature, not a “temperature of a color”. The lesson reports the expected largest rise beyond visible red and specifically discusses matching the bulb coatings and thermometer calibration. Clouds and changes in the projected optical spectrum affect the comparison. ^[ref].

For a stronger modern interpretation, an additional shaded thermometer would monitor ambient drift, exchanging bulbs between positions would test differences between thermometers, and blocking the incident beam would distinguish beam-dependent heating from warmed supports or air. These are suggested controls, not claims about Herschel's historical procedure. Thermal conduction through the mounting and convection can change the readout. A broad bulb also samples a range of wavelengths; the optical prism's transmission and optical dispersion, the bulb's absorption and heat loss all affect the position of the largest rise. In particular, the result does not show that an infrared photon carries more energy than a visible photon.

A simple analytical illustration makes those limitations explicit. Let $\theta =T-T_{\mathrm{amb}}$ be the bulb's excess temperature, $C$ its heat capacity, $G$ its effective heat-loss coefficient in $\mathrm{W}{\mathrm{K}}^{-1}$, and $P_{\mathrm{abs}}$ the absorbed power. Assume one uniform bulb temperature, constant ambient temperature, constant $C,G$, and losses linear in $\theta$. Thenfor a beam switched on at $t=0$ with $\theta (0)=0$. After switching the beam off at $t=t_s$, $\theta (t)=\theta (t_s)e^{-(t-t_s)/\tau }$. The exponential function follows by solving this linear differential equation. The steady excess temperature measures $P_{\mathrm{abs}}/G$; it is not a direct measurement of the optical spectrum. With illustrative $C=0.020\mathrm{J}{\mathrm{K}}^{-1}$ and $G=0.0010\mathrm{W}{\mathrm{K}}^{-1}$, $\tau =20\mathrm{s}$. Absorbed powers of $1.0$ and $0.5\mathrm{mW}$ give steady rises of $1.0$ and $0.5\mathrm{K}$, regardless of which wavelengths supplied that absorbed power.

The upper schematic represents the logic of the optical prism experiment; its light ray positions are not a calibrated wavelength scale. The lower curves use the illustrative heat-balance model, with the beam blocked at $60\mathrm{s}$; they are not historical or modern measured data. The beauty of the experiment is that a simple change of detector extends observation beyond what the eye can perceive.

Near a stable equilibrium bond length $r_e$, a Taylor expansion of a diatomic molecule's potential energy gives $U(r)\simeq U(r_e)+k(r-r_e{)}^2/2$, with $k=U^{\prime \prime }(r_e)>0$. Treat the internal stretch as a harmonic oscillator of reduced mass, initially omitting molecular rotation. If replacing an isotope leaves this local potential energy curvature unchanged, thenHere $c$ is the speed of light and ${\tilde{\nu }}_{\mathrm{harm}}$ a spectroscopic wavenumber; use consistent length units for $c$ and ${\tilde{\nu }}_{\mathrm{harm}}$. The quantum harmonic oscillator gives adjacent energy eigenvalues separated by $h\nu$, with $h$ the Planck constant. Consequently a vibrational photon absorption can probe the same frequency scale, subject to electric-dipole selection rules.

For an explicitly approximate isotope example, assign the atomic masses of ${}^1\mathrm{H}$, ${}^2\mathrm{H}$, ${}^{35}\mathrm{Cl}$, and ${}^{37}\mathrm{Cl}$ the mass-number values $1u,2u,35u,37u$, respectively, with $u$ the unified atomic mass unit. These are stipulated approximations to individual atomic masses, not measured masses of molecules or natural-abundance averages. They giveThe symbol $\mathrm{D}$ means deuterium, ${}^2\mathrm{H}$. Doubling the light partner's approximate atomic mass therefore produces a large predicted shift, whereas changing the already heavy chlorine partner by two mass units produces a much smaller one. A quantitative comparison with infrared spectroscopy requires actual isotope-specific atomic masses, fitted band parameters, and uncertainties, rather than identifying any arbitrary peak with ${\tilde{\nu }}_{\mathrm{harm}}$.

A Jablonski diagram arranges molecular energy eigenstates vertically and draws arrows for changes between them. In the usual closed-shell molecular example, $S_0$ is the electronic ground state, $S_1$ and $S_2$ are electronic excited states with singlet state spin, and $T_1$ has triplet state spin. Each electronic state also has levels of molecular vibration. The diagram records possible processes, not molecular paths in space.^[ref]

Photon absorption can populate an upper level of molecular vibration in $S_1$. Relaxation removes excess energy without photon emission; fluorescence commonly starts from relaxed $S_1$.^[ref] The drawing also includes relaxation from a higher electronic excited state and a competing spin-changing route to a triplet state.

The narrow reduction in photon absorption near the common resonance of opposed beams. The Doppler-free absorption line model illustrates its sign and contrast; the same feature appears as increased probe transmission.

A laser generates amplified light through stimulated emission. Its name abbreviates “light amplification by stimulated emission of radiation”. Lasers supply the intense beams used in optical tweezers; optical coherence also makes them useful for wave interference measurements. ^[ref].

In the usual material picture, a gain medium stores energy supplied by pumping, for example by incident light or an electric current. Stimulated emission transfers that stored energy to a selected optical normal mode, while competing photon absorption removes light. Producing net optical gain requires a suitable population distribution, such as population inversion in the simple model below.

A familiar laser oscillator uses mirrors to return light through the gain medium. This optical feedback favours resonant normal modes; a partly transmitting mirror lets useful power escape. Feedback and mode selection have different implementations, including ring arrangements: every laser need not resemble the same two-mirror device. The laser threshold example treats just that device. ^{[ref] [ref]}.

The useful combination is concentrated power and controlled optical normal modes. It gives optical tweezers a localized source of force and wave interference measurements a source with useful optical coherence. A laser can nevertheless emit several frequencies; “laser” alone does not guarantee a single frequency. ^[ref].

An original experimental landmark is T. H. Maiman's 1960 report of stimulated optical radiation from optically pumped ruby at about $694.3\mathrm{nm}$. His paper describes both the pumping path and the observed emission, connecting stored material energy with amplified light. ^[ref].

Laser cooling uses laser light to reduce the random velocities of chemical atoms, and therefore their translational temperature. The striking ingredient is selective photon absorption: an atom moving towards a beam sees a Doppler shift that can make it absorb more strongly. Each absorbed photon transfers momentum along the beam; repeated absorption and spontaneous emission can then remove kinetic energy. Doppler cooling makes this selection with the atom's motion, while sub-Doppler cooling also exploits its internal quantum states.

Cooling makes chemical atoms move slowly enough for longer interrogation in atomic clocks and atom interferometry, and easier loading into an optical trap. The same radiation pressure that pushes an atom can cool it: with suitably tuned opposing beams, whichever direction the atom moves, it receives the stronger push against that motion.

Laser spectroscopy uses a tunable laser to interrogate energy levels through photon absorption, stimulated emission or fluorescence. A narrow optical source is useful only if the sample and readout preserve the information: Doppler broadening can hide closely spaced spectral lines even when the source itself is narrow.

For a diatomic molecule, let $m_1,m_2$ be the two masses and $r$ their fixed separation. The distances from the centre of mass are $r_1=m_{2}r/(m_1+m_2)$ and $r_2=m_{1}r/(m_1+m_2)$. A perpendicular axis through the centre of mass therefore has moment of inertiaThe reduced mass $\mu$ here is not the electric dipole moment, for which we use $\mathbf{d}$. For a longer linear molecule, replace $\mu r^2$ by ${\sum }_i{m}_i{\rho }_i^2$, where ${\rho }_i$ is each distance along the axis from the centre of mass. In the point-mass idealization, the axial moment of inertia is zero; turning about that axis changes no nuclear positions, so no independent axial rotational degree of freedom is included.

For the field-free linear rigid rotor, assume a fixed internal quantum state with no electronic angular momentum or electronic spin, and omit couplings to nuclear spin. The rotational Hamiltonian is ${\hat{H}}_{\mathrm{rot}}={\hat{\mathbf{L}}}^2/(2I)$. Its orientation wavefunctions are spherical harmonics $Y_{JM}$, and its angular momentum eigenstates satisfywhere $J=0,1,2,\dots$ and $M=-J,-J+1,\dots ,J$. Each $E_J$ belongs to $2J+1$ angular momentum eigenstates distinguished by the magnetic quantum number $M$, an instance of degenerate energy levels. The Planck constant is $h=2\pi \hslash$; $B$ is the frequency-valued rotational constant. Notice that the energy eigenvalues scale as $J(J+1)$, not $J^2$.

Subtracting consecutive energy eigenvalues givesThus increasing level gaps produce a regularly spaced series of lines at $2B,4B,6B,\dots$, with spacing $2B$. Allowed positions do not guarantee that every line is visible: electric-dipole selection rules, occupation of the initial quantum state, and instrument response also matter.

Robert Andrews Millikan's 1916 experiment used a magnetically turned wheel and rotary knife to expose sodium or lithium in vacuum. A surrounding copper-gauze/solid-copper collector caught electrons; an electrometer recorded accumulated electric charge over thirty seconds at each applied voltage. He located endpoints graphically from photocurrent curves. Mercury spectral lines, selected by a monochromator and filters, controlled frequency; rejecting shorter-wavelength contamination protected the endpoint. An oxidized collector suppressed reverse emission for selected lines. A copper test plate measured the contact potential difference by a displacement-null method; a certified voltmeter set the electrical scale. He compared stable-surface sweeps with rapid alternating-frequency measurements to control drift. The slope tested $h/e$; the threshold required the contact correction. His gauge did not measure mercury vapor. Confirmation of the equation coexisted with his continued skepticism about localized light quanta.^[ref]

For a modern repetition of the logic, first establish electrical zero with the illumination blocked, characterize leakage, and verify the voltmeter scale independently of the presumed Planck constant. Scan several voltages near each endpoint rather than calling one noisy zero a cutoff. Hold the illuminated area and surface state fixed when varying light intensity; vary frequency independently when testing the slope. Repeating a reference frequency between other readings reveals time-dependent offsets. Agreement of a slope with $h/e$ tests an energy relation; it does not alone identify every microscopic step of photon absorption and escape.

Optical gain is amplification of light by a medium. Here the small-signal intensity gain coefficient $g$ has units ${\mathrm{m}}^{-1}$: for fixed populations, a weak beam obeysin the nondegenerate resonant two-level model, with common transition cross-section $\sigma$. Thus $g$ includes the competition between stimulated emission and photon absorption on that transition. Separate passive intensity loss $\alpha$ gives $I(z)=I(0)e^{(g-\alpha )z}$. Both coefficients describe light intensity, not wave amplitude; the corresponding field-amplitude exponent is half as large. ^[ref].

For $g=0.30{\mathrm{m}}^{-1}$, $\alpha =0.10{\mathrm{m}}^{-1}$ and $z=0.50\mathrm{m}$, the single-pass intensity multiplier is $e^{0.10}\approx 1.10517$. This is amplification during one passage, before mirror losses. Population inversion can therefore yield positive optical gain while the complete oscillator remains below laser threshold.

Optical pumping redistributes populations among internal quantum states by selective photon absorption followed by spontaneous emission. It can prepare atoms for measurement and participate in sub-Doppler cooling.

The practical aim is to make otherwise almost equally populated magnetic sublevels behave differently. Repeated absorption and emission can store a population imbalance in the long-lived ground state; a change in photon absorption or fluorescence then reveals a perturbation of that prepared distribution. This combines preparation and measurement: a weak radio wave can reorganize the populations, while abundant optical photons supply the readout.

An imbalance among ground state magnetic sublevels need not be a population inversion between optical energy levels. Optical pumping also supplies excitation in some lasers, where an appropriate population inversion matters for gain. The preparation problem here concerns the distribution within the ground state. A two-level system with only one lower quantum state cannot describe this redistribution.

Circular polarization selects the sign of the absorbed photon's angular momentum along the beam. Choose that direction as $z$ and define ${\sigma }^{+}$ by the absorption rule $m^{\prime }=m+1$, where $m$ is the magnetic quantum number. Spontaneous emission can return an atom to a different magnetic sublevel, so absorption followed by emission is a population-transfer cycle. A sublevel that the chosen beam cannot excite is dark to that beam. Darkness is relative to the selected transition and electromagnetic polarization, rather than a claim that the atom cannot interact with any light.

A static magnetic field along $z$ defines a stable axis and gives Zeeman splitting. A transverse oscillating magnetic field can redistribute magnetic sublevel populations when its frequency matches an allowed splitting. With the appropriate optical transition, that redistribution restores photon absorption: transmitted intensity decreases, or collected fluorescence increases. These are alternative readouts whose detailed sensitivity depends on the transition, viewing direction and electromagnetic polarization.

A three-level laser uses a pump transition from ground level1 to a higher level3, rapid relaxation $3\to 2$, and a long-lived upper lasing level2. The laser transition is $2\to 1$, so its lower level is the ground state. Fast feeding and slow upper-state decay allow excitation to accumulate, unlike steady resonant pumping of a simple two-level transition.

Stimulated emission adds photons to the stimulating optical mode, but ground-state photon absorption competes with it. The population inversion condition is $N_2/g_2>N_1/g_1$ when the relevant transition strengths obey the usual Einstein relations. For equal degeneracies and negligible $N_3$, it reduces to $N_2>N_1$, requiring more than half the active population in level2.

For a simple pump rate R per ground-state emitter, fast $3\to 2$ relaxation and negligible laser intensity, the three-level laser rate equation reduces toThis three-level ground-state inversion threshold is only transparency; positive gain must also overcome optical losses. For an illustrative uniformly filled cavity of length $\ell$, equal absorption/emission cross-section $\sigma$, internal intensity-loss coefficient ${\alpha }_i$ and mirror power reflectivities $R_1,R_2$, the threshold condition isHere $n_i$ are number densities, unlike the total populations $N_i$. The optical resonator supplies feedback and selects modes; a partially transmitting mirror couples out light. Spontaneous emission seeds the field, and stimulated transitions deplete the inversion until saturated gain balances loss. A ruby laser is the standard example. Real level degeneracies, branching losses and pump saturation modify the simple equations. ^[ref]

A useful organizing principle is Gibbs free energy: at specified temperature and pressure a coupled process is favorable when its total $\Delta G$ is negative. For each chemical species,The relative amounts of chemical substances determine the available Gibbs free energy, beyond counting energy in individual bonds. Nutrient oxidation and light-driven chemistry can maintain nonequilibrium compositions. ATP hydrolysis can drive biosynthesis, transport and motion of molecular motors when reactions are coupled so that their total free-energy change is favorable. Breaking an inorganic phosphate bond itself costs energy; the favorable net hydrolysis includes formation and solvation of the products and depends on their thermodynamic activities.

Redox Gibbs free energy comes from transferring electrons between donors and acceptors: $\Delta G=-nF\Delta E$. Electron transfer in respiration or photosynthesis can help establish an electrochemical gradient. For a mole of ions moving from side 1 to side 2,The concentration and electrical terms together drive transport and can power ATP synthase. ATP-driven pumps can conversely build gradients. Chemiosmosis is the coupling between this gradient and chemical synthesis, not the creation of Gibbs free energy by an enzyme.

Mechanical work and elastic storage are other forms: a motor can do $\int Fdx$ or $\int \tau d\theta$, and an approximately Hookean element stores $k{x}^2/2$. ATP-driven motors convert Gibbs free energy into motion, while externally forced reverse motion can sometimes drive chemical synthesis. A photon brings energy $h\nu$; light photon absorption initiates chemistry in photosynthesis and light-driven pumps, with some energy inevitably dissipated. Living cells use these conversions for structure, movement, homeostasis and synthesis, while releasing heat and exporting entropy. At a single uniform temperature, dissipated heat cannot be completely recycled into useful work.